Physics Vectors Overview

so welcome to part two of lecture two introduction of physics so in this video we're going to discuss some of the concepts related to vectors quantities in physics may either be scalar or a vector so when we say scalar quantities they are quantities which are described by the magnitude and their respective units while vectors is described by magnitude appropriate units and with direction so it means to be in vector quantities are quantities which can be associated with direction while if that quantity cannot be associated with direction then that quantity is a scalar quantity so let us look at the common examples so for example for scalar quantities we have the temperature so temperature is measured in degrees celsius for example 39 degrees celsius now can we associate uh the direction can we associate direction to the measure of temperature so can we describe 39 degrees Celsius north or 39 degrees Celsius south. degrees Celsius East so it doesn't make sense so therefore temperature cannot be associated with direction the same with time so a la naman time time na na one hour north one hour is the device the same with other scalar quantities so he makes a real scalar quantities are quantities which cannot be associated with direction so I mean description long yeah is the magnitude and the respecting units of that magnitude while for vector these are the common examples we have weight velocity force displacement acceleration momentum and torque so for example c4 so when for example we applied 10 newtons to one side of an object so of course the direction of the of the force is to the direction to to it's the same with the direction where you applied the force for example nag apply can and ten newtons is then the direction is of the forces is so velocity no man is when you apply direction to the speed so coppock nag apply can an on direction to the magnitude to the magnitude of speed then that is not the speed that becomes velocity and velocity for example a car moving seven kilometers per hour due north so you can be be in 17 kilometers per hour North you velocity nia pero kapag speed lamb on description along is 7 kilometers per hour wall on the action so again vector quantities are quantities which can be described by its magnitude appropriate units and the associated direction while scalar quantities is described only by the magnitude and their respective units to represent a vector we use a line with an arrowhead so arrowed line and then the direction of the arrowhead indicates the direction of the quantity so for vector a the direction is east for vector b's direction is west so if it is pointed up the direction is north if it is down the direction is south and then relative to the north east west south line the direction is northeast northwest southeast and southwest the length of the arrow is scaled to be proportional to the magnitude of the vector quantity represents so for example we have here vector a and vector b so vector a is shorter than vector b so meaning the magnitude of of vector a is less than vector So, meaning kapag maiksi lang yung arrow, yung arrow ng vector, ibig sabihin mababa din yung value. you know magnitude couple Mahaba you are oh you mean something in Malakia didn't you magnitude no better more quantity vector quantities are denoted by a letter so usually capital letter with an arrow head above above the letter or a bold face letter so it oh but then you represent you vector using a copy letter with an arrowhead above or using a boldface letter so naka control be nice and a couple boldface you letters so that denotes a vector quantity while the magnitude of a vector is represented by a light-faced letter without an arrowhead on top. So, again, so magnitude of a vector is represented by a light-faced letter without an arrowhead on top or the symbol of the vector placed inside a vertical. bar vertical side so ito diba naka bold sya so kapag naka light face naman sya ang ibig sabihin nya that symbol symbolizes the magnitude of a vector okay Or to represent the magnitude of a vector, we can place this vector symbol within a vertical bar or we can place this bold-faced platter within a vertical bar. So that is the representation of the magnitude of a vector. so how do we locate or how do we determine the direction of a vector so the direction of a vector is the acute angle it creates with the east west line or the acute angle it creates with respect to the x-axis or with respect to the horizontal axis. So take note that the acute angles are angles less than 90 degrees. So in this case, for the vector, the acute angle is measured with respect to the x-axis or the east-west line. So if we have this diagram, so this is our east-west line so horizontal in x-axis not and that is the east-west line so on another acute angle not and is measured so with respect to this horizontal line so if the arrow is pointing towards the northeast then our our acute angle is this side so it means the arrow is not is found north east so this is the angle so the vector A is found north of west and then the vector is found south of west and south of east The letter N or North and South and South is written after the measure of the angle followed by the phrase of E for East and of W for West. So for example, 60 degrees. degrees S of W so this is the measure of angle followed by South or if the direction is North then North is what you will put there and followed by of W or of E so in this example 60 degrees South S of W means that starting from West you go down by 60 degrees so let's go back to here so it means that the arrow the direction of the arrow for that particular example is starting from the west line so yeah starting from the west line the arrow is 60 degrees south of west yeah so with respect to the the west line so example so let's determine the direction direction of vector a and direction of vector b so the vector a nakita natin that it is directed north of east so pano is to select you and then you direction yeah so direct the direction of vector a so we're not in a and so with respect to the east line vector a is 30 degrees north of the East line so therefore Kapang sinulat natin a is 30 degrees n of e while CB no man with respect to the east-west line so since Anita some my West line with respect to the West line vector B is 45 degrees south of West So let's answer the following. So let's determine the direction of the vectors A, B, C, and D. So ano kaya yung direction nitong mga vectors? So you can pause this video and then go back kapag nasagutan nyo na yung itong activity na to. Okay, so to answer this activity, vector A with respect to vector B, to the east line is 50 degrees 50 degrees north of the east line so a is 50 degrees north of east while b so on reference namanatin dito with respect to the west line so b is 45 degrees 45 degrees north of the west line so answer is 45 degree n of w so c no man is 20 degrees south of the east line so south of the east line and then d is simply south directed south so how do we represent vectors in graphs so step one so we can do the following steps we Create a Cartesian plane and then identify to which quadrant in the Cartesian plane will the vector lies using the given direction of the vector. So, kanina, kung kanina meron tayong, asa na yun? So, kanina meron tayong given graph tapos we identify the direction. Then, to represent it, so for example, given naman ito, paano naman natin siya ire-represent dito sa graph? so you know so step one we create a cartesian plane so it is important to familiarize yourself with the cartesian plane step two is using a protractor measure and mark the angle with respect to the x axis so along or along the east west line so yeah you need prior knowledge on how to use protractor and then step three is to draw a line connecting the point of origin and with the markings of the measured angle so if the magnitude is given measure it to scale so measure the length of the vector so familiarization with the cartesian plane and on how to use a protractor is helpful in graphically representing a vector so here we have a cartesian plane so this is the y-axis and this is the x-axis so here is in this direction it points towards the east and this direction points towards the west this points towards the north and this is south so the cartesian plane is divided into four quadrants so the positive positive side is quadrant one so the negative positive side is quadrant two negative negative side is quadrant three and positive negative side is quadrant four so So meron tayong quadrant 1, quadrant 2, quadrant 3, and then quadrant 4. so that's the description so just read it in your modules so one rotation or one revolution from the positive axis to one counterclockwise revolution or even clockwise revolution so one revolution or one rotation in the cartesian plane represents 360 degrees so that's the measurement so therefore therefore if we divide it into four quadrants so each quadrant measures 90 degrees so the first quadrant is from 0 to 90 degrees the second quadrant is from 90 degrees to 180 degrees later i will show you the diagram and then the third quadrant is from 180 degrees to 270 degrees and the fourth quadrant is from 270 degrees to 360 degrees so later my my kitten at and come back at the Lama not an um familiarize also the degrees of each of the line each of this direction okay so i So to use a protractor, so wala akong video. So ito na lang. So to use a protractor, ayan. so what you will do first is make sure that this is the line or there is a line below the protractor and then there is a cross mark so the center of that cross is the one with holes so that represents the point of origin so make sure that the horizontal line and the the horizontal line and the vertical line aligns with your with the Cartesian plane. So if you want to measure for example 10 degrees north of east so from this side, you need to read this this one inside so you will start from zero zero degrees, ten degrees, twenty degrees, thirty degrees, forty, fifty, sixty, seventy, eighty, ninety so if you want to determine the angle then from 0 degrees ito naman nasa outer numbers labels so 0 degrees this is 10 degrees this is 20 degrees 30 40 50 60. so yan ang susundan mo kapag baliktad naman example ayan so baliktad naman so make sure na ayan pag binaliktad mo magbabasa mo parin yung numbers correctly so ito this is 10 degrees so dito naman magbabase ka sa outer number so if you are in quadrant 4, you will base on the outer number 10, 20, 30, 40, 50, 60, 70, 80 and then here on the inner calibration so 10, 20, 30, 40, 50, 60, 70, 80 to 90 so each of these are 90 degrees horizontal and the horizontal and vertical line are 90 degrees with respect to each other and in total 90 90 plus 90 plus 90 is equal to 360 degrees yeah so for example it don't i know nothing it don't vector nothing yeah so not 130. or for example, I put it here on the other side, its measure is not 120 it is 60 degrees so the same with this side for example in this side I put it here I put it for example here in the middle of this so this side this vector is 40 degrees with respect to our west line so here on the other side ibig sabihin ito this is kunwari nasa 30 so ibig sabihin ito that this vector is 30 degrees with respect to the west line so ang movement ng pagbilang is from the east west line so 10 20 30 and 10 20 30. okay so example so example so graphically represent vector a which is directed 30 degrees north of east so north of east is found in quadrant one so ayan ang ating north of east so dito quadrant one so ibig sabihin the direction is north of east pero paano natin i represent yung 30 degrees north of east so we make use of our i told you to protractor so dito i already place a mark marking so from the east line magbilang tayo ng 30 degrees so 10 20 30 degrees so lagyan mo ng marka and then next is to connect yeah so using a ruler so to scale for example for example my scale niana may run by integration for example what for every one centimeter even sabine nyan i one kilometer equivalent to one kilometer so to toon scenario then you can already i know do it so measure you know how about the drawing kayo nang nang vector so therefore our or to represent vector a which is directed 30 degrees north of east so this is the graphical representation so this is the angle created by vector a with respect to the east line so to look for to to identify also or to to have an example for the other direction so other quadrants so let us look for the following let us represent the following vectors in our graph so vector a is 78 degrees south of east so since this is south of east so saan yung south? so ito yung south and this is east so ibig sabihin andito siya mahanap sa kwadrant number 4 so using a protractor hanapin natin si 78 degrees so this is 10 20 from the east line bilang tayo 10 20 30 40 50 60 70 and then i am so each markings graduation is one degree so therefore and it was a 78 degree so markahan you know and then the pangdugtugi trace you know so therefore this line so this vector now represents vector a which is 78 degrees south of east so yeah in direction so how about it all cb is 39 degrees north of west excuse me so north of west is found little second quadrant not tense this is the west line so nasaan ang north ng west line andito sya sa kwadran 2 so Next is to measure yung 39 degrees. So since andyan sya, then kapag hinanap naman natin sya, eto. So with respect to the west line, magbilang tayo ng 39 degrees. So 10, 20, 30, and then 35, and then 36, 37, 38, 39. So andyan yung 39 degrees. Then connect the line. So using a ruler. So, to represent this vector with its direction in a graph, in a diagram. So, ayan na yung kanyang direction. And last, vector C is 15 degrees south of west. So, south of west, this is our west line. Nasa ng south ng west line. So, nasa andito. So, nasa quadrant 3. So, we need to measure 15 degrees south. of west with respect to the west line so using our protractor this is 10 degrees and then ito 10 11 12 10 11 12 13 14 15 degrees so this is So, maglagay kayo ng marking dun sa 15 degrees. And then, trace it using your ruler so yeah so this is vector c so vector c is 39 degrees or 39 degrees south of the west line to find so how do we find the direction of vectors with angles in standard form so for example here we are giving direction with north, east, south, west so there is association of north, east, south, west so not just angle so what if the angle given is not with respect to the east-west line but with respect to the one revolution one rotation in the Cartesian plane to find the direction of vectors with angles in standard form we need to solve for the value of the reference angle so reference angle this is the the the acute angle smallest positive acute angle with respect to the x-axis or with respect to the east west line so to solve for a new before we we go to the equations for the reference angle or the formula for reference angle so ito pala yung kanina so again so review all it nothing new new cartesian plane so it is divided by the vertical y-axis and the horizontal line x-axis so each of this the the intersection of this vertical and horizontal line created four 90 degree angles since they are perpendicular to each other so 90 degree plus 90 degree plus 90 degree plus 90 degrees equal to 360 degrees so one rotation or one revolution in our cartesian plane will create 360 degree angle so from from the east line to the north line From the east line to the north line, so meron tayong 0 degree to 90 degree. From the north line to the west line, ang measure natin is 90 degree to 180 degree. And from the west line to the south. line well 180 degree to 270 degree and from the south line to the east line we complete one revolution so 270 degree to 360 degrees so this angle is with respect to the one rotation or one revolution along the cartesian plane so from positive x moving to the positive x so standard angle or angles following the 360 degree angle of one revolution so while the reference angle is the smallest positive acute angle with respect to the horizontal axis so to look for the reference angle we can use the following formula so it depends on the given situation of the given angle so if our if the given standard angle is less than 90 degrees then our reference angle is equal to the standard angle so it means Sabihin, kapag ang angle mo is less than 90 degrees, yun na din yung reference angle mo. And the location of that, of the vector is in quadrant 1 or in northeast. north of the east line. Kapag yung given angle mo, if the standard angle is greater than 90 degrees but less than 180 degrees, to look for the value of the reference angle or the smallest positive acute angle, we subtract the standard angle from 180. So 180 degrees minus the given angle is equal to the reference angle. So in this situation, kapag ganyan, kapag yung angle mo is greater than 90 but is less than 180, then the vector is found in quadrant 2. So ang quadrant 2, ang direction nya is north of the west line. Kapag naman yung given angle mo is greater than 180 but less than 270 degrees, then to look for the reference angle or the value of the acute angle we use this equation so formula so given angle or the standard angle minus 180 degrees so this situation where the given angle or the standard angle is greater than 180 but less than 270 degrees can be located the vector can be located in quadrant number three So where in the description is South of the west line. Kapag naman yung ano, when the given angle is greater than 270 degrees, to look for the reference angle, we subtract the given angle from 360. So 360 minus the standard angle will will yield to the reference angle so when when standard angle is greater than 270 the vector is found in quadrant 4 so the description for quadrant 4 the direction is south of the east line so let us have the following example so find the direction of vector n when n is located at angle of 220 degrees so 220 so 220 is greater than 180 but 220 is less than 270. so if we go back to our table this is the situation So, yung 220 is greater, mas malaki siya kay 180, pero maliit siya kumpara kay 270. Therefore, to find the value of our reference angle, we use this equation. reference angle is equal to the given angle minus 180 so 220 degrees our given angle which is a standard angle minus 180 is equal to 40 degrees therefore the direction of our vector is 40 degrees so if we will put it in a graph so this is it so 220 that is the reference standard angle nothing with respect to one revolution so meaning little 90 degree 180 degree and then 220 degree so that so the tonight in my hand up young angle not 10 so 220 degree so we we looked for the the value of reference angle to describe the direction of vector n so since and it is a quadrant number three mahana then the direction is south of west and the value with respect to the west line the the ref the the angle created with this by this vector is 40 degrees. Therefore, N is 40 degrees south of west. It is located 40 degrees south of the west line so for other examples we have other examples in our anyways Nasa ibang ano ata nasa kabila ata file. So dun sa module nyo madami pa dyan example. so you can familiarize yourself with it so just remember this rule if the angle you gave is an angle with respect to the 360 degree so how will you know that with respect to the 360 degree or panino malala man a standard angle and given sign you condition of BB gain on iron non north of east non location yeah quadrants so this is a BB vehicle north of East Basha north of West south of West or south of East yeah so you know rules so you know you know you condition and these are the equations for that rule so let's discuss the magnitude of a vector so vector has a magnitude and if a magnitude is given we write it using a light-faced letter or the symbol of vector enclosed in vertical bar so kanina pinakita ko na yan sa iyo so if the numerical value is given we write write the value so this is the symbol of the magnitude representation of the magnitude of a vector excuse me and then yes example so So vector n is n 40 degrees south of west. So this is the quantity. This is the value of the vector. So when we say magnitude of a vector, it talks about the length of the vector. so that length can be measured in different with different units can be associated with different units so kapag naman daw number numerical value ang binigay then we replace the letter with the numerical value so for example vector n is 25 kilometers 40 degrees south of west so the length of the vector the magnitude of a vector is the length the measure of the length of a vector so if a vector is to scale we can measure the actual magnitude of that vector using a measuring device so for example if one kilometer so if one kilometer is scaled to one centimeter then in a ruler every one centimeter is equivalent to one kilometer so kapag kapag ang vector mo is two centimeters long ibig sabihin sa totoong ano in real situation so in real situation that corresponds to two kilometers so so you can also use other units here so for example one newton a one centimeter is equivalent to one newton so in and then For example, we have an arrow. that is four centimeters long so it means if you measure the arrow using a ruler and then four centimeters long then that means that our arrow is four kilometers in real life so right if in real life We are not drawing, we are not measuring the 1 kilometer in the bond paper for example. So this concept is also used in maps for example here. So we have scales. So for example this. So every graduation this means that this is equivalent to kilometers if you measure it it is equivalent to kilometers the same with this one the scale in our map so here, every 1 cm our scale is 1 cm is to 1 km so meaning, every 1 cm in our ruler is equivalent to 1 km so it can be every 1.5 cm or every 0.5 cm is equivalent to one kilometer so you can decide how you want to scale your measurements so there are different types so four types of vectors first is the equal vectors equal vectors are when two vector i saw so two vectors are equal if they have the same magnitude and direction so in in graphical representation so the direction of the vectors are pointing so that the vectors are pointing towards the same direction so equal yung direction and the same direction and then the same din yung magnitude so ito 4 kilometers Vector A and Vector B are pointing towards the east side. Therefore, Vector N and Vector B are equal. They can also be equal but pointing towards the north. So, they should be in the same direction and the same magnitude. The second type of vector is the parallel vector. So, two vectors are parallel. if they have the same direction but may have different magnitude so they are pointing towards the same direction but one is longer and the other is shorter for example vector a is three kilometers towards east then b vector b is four kilometers towards the east so they are parallel vectors since they are pointing towards in the same direction anti-parallel vectors if they have an angle between if the angle between the vectors is but bucket one thousand times 180 degrees degrees da pato if the angle between the vectors is 180 degrees or if they are pointing towards the polar opposite of each others for example it only suck it don't miss up is pointing towards the West while the other one is pointing towards the east so this is also an example of anti-parallel so or you miss up pointing towards the north you miss up pointing towards the south or further in the manual so further in the manner ganyan so you miss a pointing towards the south of west is a pointing towards the north of east so these are anti-parallel vectors and the last type of vector is so before we go to the last type of vector so equal vectors parallel vectors and anti-parallel vectors are collinear vectors so it means the vectors lie in the same line of action for example This is the line of action. So, they are both horizontal. Or they are both diagonal. They are both vertical vectors. So, the last type of vector is the non-collinear vector. So, two vectors are non-collinear if they are on the same plane but not acting on the same line of action. So these vectors are separated by an angle that is not equal to 0 and not equal to 180 degrees. so for example is the right vectors divided separated by 90 degree angle so you miss up pointing towards the north you miss a number pointing towards the east or putting kites and direction as long as right angle so any vector separated by a right angle or nine separated by 90 degrees or non-collinear vectors so any vectors that are perpendicular to each other are non-collinear vectors so any acute any vectors um divided or separated by an acute angle so if we say acute angle those are angles that are less than 90 degrees for example 45 89 and below so that but not equal to zero so acute angle vectors that are separated by an acute angle is a non-collinear vectors and the same with the obtuse with obtuse angles so two vectors separated by an obtuse angle so kapag obtuse those are angles that are greater than 90 degrees so 91 92 93 94 but not equal to 180 degrees so any two vectors separated by an obtuse angle is a non-collinear so that is all for this part two of vectors so in our next video we're going to discuss vector addition and then representing vectors in component form so paano tayo mag-a-add ng vectors adding two vectors or adding two or more vectors and how do we use the different methods of vector addition so thank you for listening

So, again, so magnitude of a vector is represented by a light-faced letter without an arrowhead on top or the symbol of the vector placed inside a vertical. bar vertical side so ito diba naka bold sya so kapag naka light face naman sya ang ibig sabihin nya that symbol symbolizes the magnitude of a vector okay Or to represent the magnitude of a vector, we can place this vector symbol within a vertical bar or we can place this bold-faced platter within a vertical bar. So that is the representation of the magnitude of a vector. so how do we locate or how do we determine the direction of a vector so the direction of a vector is the acute angle it creates with the east west line or the acute angle it creates with respect to the x-axis or with respect to the horizontal axis. So take note that the acute angles are angles less than 90 degrees.

So in this case, for the vector, the acute angle is measured with respect to the x-axis or the east-west line. So if we have this diagram, so this is our east-west line so horizontal in x-axis not and that is the east-west line so on another acute angle not and is measured so with respect to this horizontal line so if the arrow is pointing towards the northeast then our our acute angle is this side so it means the arrow is not is found north east so this is the angle so the vector A is found north of west and then the vector is found south of west and south of east The letter N or North and South and South is written after the measure of the angle followed by the phrase of E for East and of W for West. So for example, 60 degrees. degrees S of W so this is the measure of angle followed by South or if the direction is North then North is what you will put there and followed by of W or of E so in this example 60 degrees South S of W means that starting from West you go down by 60 degrees so let's go back to here so it means that the arrow the direction of the arrow for that particular example is starting from the west line so yeah starting from the west line the arrow is 60 degrees south of west yeah so with respect to the the west line so example so let's determine the direction direction of vector a and direction of vector b so the vector a nakita natin that it is directed north of east so pano is to select you and then you direction yeah so direct the direction of vector a so we're not in a and so with respect to the east line vector a is 30 degrees north of the East line so therefore Kapang sinulat natin a is 30 degrees n of e while CB no man with respect to the east-west line so since Anita some my West line with respect to the West line vector B is 45 degrees south of West So let's answer the following. So let's determine the direction of the vectors A, B, C, and D.

So ano kaya yung direction nitong mga vectors? So you can pause this video and then go back kapag nasagutan nyo na yung itong activity na to. Okay, so to answer this activity, vector A with respect to vector B, to the east line is 50 degrees 50 degrees north of the east line so a is 50 degrees north of east while b so on reference namanatin dito with respect to the west line so b is 45 degrees 45 degrees north of the west line so answer is 45 degree n of w so c no man is 20 degrees south of the east line so south of the east line and then d is simply south directed south so how do we represent vectors in graphs so step one so we can do the following steps we Create a Cartesian plane and then identify to which quadrant in the Cartesian plane will the vector lies using the given direction of the vector.

So, kanina, kung kanina meron tayong, asa na yun? So, kanina meron tayong given graph tapos we identify the direction. Then, to represent it, so for example, given naman ito, paano naman natin siya ire-represent dito sa graph? so you know so step one we create a cartesian plane so it is important to familiarize yourself with the cartesian plane step two is using a protractor measure and mark the angle with respect to the x axis so along or along the east west line so yeah you need prior knowledge on how to use protractor and then step three is to draw a line connecting the point of origin and with the markings of the measured angle so if the magnitude is given measure it to scale so measure the length of the vector so familiarization with the cartesian plane and on how to use a protractor is helpful in graphically representing a vector so here we have a cartesian plane so this is the y-axis and this is the x-axis so here is in this direction it points towards the east and this direction points towards the west this points towards the north and this is south so the cartesian plane is divided into four quadrants so the positive positive side is quadrant one so the negative positive side is quadrant two negative negative side is quadrant three and positive negative side is quadrant four so So meron tayong quadrant 1, quadrant 2, quadrant 3, and then quadrant 4. so that's the description so just read it in your modules so one rotation or one revolution from the positive axis to one counterclockwise revolution or even clockwise revolution so one revolution or one rotation in the cartesian plane represents 360 degrees so that's the measurement so therefore therefore if we divide it into four quadrants so each quadrant measures 90 degrees so the first quadrant is from 0 to 90 degrees the second quadrant is from 90 degrees to 180 degrees later i will show you the diagram and then the third quadrant is from 180 degrees to 270 degrees and the fourth quadrant is from 270 degrees to 360 degrees so later my my kitten at and come back at the Lama not an um familiarize also the degrees of each of the line each of this direction okay so i So to use a protractor, so wala akong video.

So ito na lang. So to use a protractor, ayan. so what you will do first is make sure that this is the line or there is a line below the protractor and then there is a cross mark so the center of that cross is the one with holes so that represents the point of origin so make sure that the horizontal line and the the horizontal line and the vertical line aligns with your with the Cartesian plane. So if you want to measure for example 10 degrees north of east so from this side, you need to read this this one inside so you will start from zero zero degrees, ten degrees, twenty degrees, thirty degrees, forty, fifty, sixty, seventy, eighty, ninety so if you want to determine the angle then from 0 degrees ito naman nasa outer numbers labels so 0 degrees this is 10 degrees this is 20 degrees 30 40 50 60. so yan ang susundan mo kapag baliktad naman example ayan so baliktad naman so make sure na ayan pag binaliktad mo magbabasa mo parin yung numbers correctly so ito this is 10 degrees so dito naman magbabase ka sa outer number so if you are in quadrant 4, you will base on the outer number 10, 20, 30, 40, 50, 60, 70, 80 and then here on the inner calibration so 10, 20, 30, 40, 50, 60, 70, 80 to 90 so each of these are 90 degrees horizontal and the horizontal and vertical line are 90 degrees with respect to each other and in total 90 90 plus 90 plus 90 is equal to 360 degrees yeah so for example it don't i know nothing it don't vector nothing yeah so not 130. or for example, I put it here on the other side, its measure is not 120 it is 60 degrees so the same with this side for example in this side I put it here I put it for example here in the middle of this so this side this vector is 40 degrees with respect to our west line so here on the other side ibig sabihin ito this is kunwari nasa 30 so ibig sabihin ito that this vector is 30 degrees with respect to the west line so ang movement ng pagbilang is from the east west line so 10 20 30 and 10 20 30. okay so example so example so graphically represent vector a which is directed 30 degrees north of east so north of east is found in quadrant one so ayan ang ating north of east so dito quadrant one so ibig sabihin the direction is north of east pero paano natin i represent yung 30 degrees north of east so we make use of our i told you to protractor so dito i already place a mark marking so from the east line magbilang tayo ng 30 degrees so 10 20 30 degrees so lagyan mo ng marka and then next is to connect yeah so using a ruler so to scale for example for example my scale niana may run by integration for example what for every one centimeter even sabine nyan i one kilometer equivalent to one kilometer so to toon scenario then you can already i know do it so measure you know how about the drawing kayo nang nang vector so therefore our or to represent vector a which is directed 30 degrees north of east so this is the graphical representation so this is the angle created by vector a with respect to the east line so to look for to to identify also or to to have an example for the other direction so other quadrants so let us look for the following let us represent the following vectors in our graph so vector a is 78 degrees south of east so since this is south of east so saan yung south?

so ito yung south and this is east so ibig sabihin andito siya mahanap sa kwadrant number 4 so using a protractor hanapin natin si 78 degrees so this is 10 20 from the east line bilang tayo 10 20 30 40 50 60 70 and then i am so each markings graduation is one degree so therefore and it was a 78 degree so markahan you know and then the pangdugtugi trace you know so therefore this line so this vector now represents vector a which is 78 degrees south of east so yeah in direction so how about it all cb is 39 degrees north of west excuse me so north of west is found little second quadrant not tense this is the west line so nasaan ang north ng west line andito sya sa kwadran 2 so Next is to measure yung 39 degrees. So since andyan sya, then kapag hinanap naman natin sya, eto. So with respect to the west line, magbilang tayo ng 39 degrees.

So 10, 20, 30, and then 35, and then 36, 37, 38, 39. So andyan yung 39 degrees. Then connect the line. So using a ruler. So, to represent this vector with its direction in a graph, in a diagram.

So, ayan na yung kanyang direction. And last, vector C is 15 degrees south of west. So, south of west, this is our west line. Nasa ng south ng west line. So, nasa andito.

So, nasa quadrant 3. So, we need to measure 15 degrees south. of west with respect to the west line so using our protractor this is 10 degrees and then ito 10 11 12 10 11 12 13 14 15 degrees so this is So, maglagay kayo ng marking dun sa 15 degrees. And then, trace it using your ruler so yeah so this is vector c so vector c is 39 degrees or 39 degrees south of the west line to find so how do we find the direction of vectors with angles in standard form so for example here we are giving direction with north, east, south, west so there is association of north, east, south, west so not just angle so what if the angle given is not with respect to the east-west line but with respect to the one revolution one rotation in the Cartesian plane to find the direction of vectors with angles in standard form we need to solve for the value of the reference angle so reference angle this is the the the acute angle smallest positive acute angle with respect to the x-axis or with respect to the east west line so to solve for a new before we we go to the equations for the reference angle or the formula for reference angle so ito pala yung kanina so again so review all it nothing new new cartesian plane so it is divided by the vertical y-axis and the horizontal line x-axis so each of this the the intersection of this vertical and horizontal line created four 90 degree angles since they are perpendicular to each other so 90 degree plus 90 degree plus 90 degree plus 90 degrees equal to 360 degrees so one rotation or one revolution in our cartesian plane will create 360 degree angle so from from the east line to the north line From the east line to the north line, so meron tayong 0 degree to 90 degree.

From the north line to the west line, ang measure natin is 90 degree to 180 degree. And from the west line to the south. line well 180 degree to 270 degree and from the south line to the east line we complete one revolution so 270 degree to 360 degrees so this angle is with respect to the one rotation or one revolution along the cartesian plane so from positive x moving to the positive x so standard angle or angles following the 360 degree angle of one revolution so while the reference angle is the smallest positive acute angle with respect to the horizontal axis so to look for the reference angle we can use the following formula so it depends on the given situation of the given angle so if our if the given standard angle is less than 90 degrees then our reference angle is equal to the standard angle so it means Sabihin, kapag ang angle mo is less than 90 degrees, yun na din yung reference angle mo. And the location of that, of the vector is in quadrant 1 or in northeast.

north of the east line. Kapag yung given angle mo, if the standard angle is greater than 90 degrees but less than 180 degrees, to look for the value of the reference angle or the smallest positive acute angle, we subtract the standard angle from 180. So 180 degrees minus the given angle is equal to the reference angle. So in this situation, kapag ganyan, kapag yung angle mo is greater than 90 but is less than 180, then the vector is found in quadrant 2. So ang quadrant 2, ang direction nya is north of the west line. Kapag naman yung given angle mo is greater than 180 but less than 270 degrees, then to look for the reference angle or the value of the acute angle we use this equation so formula so given angle or the standard angle minus 180 degrees so this situation where the given angle or the standard angle is greater than 180 but less than 270 degrees can be located the vector can be located in quadrant number three So where in the description is South of the west line.

Kapag naman yung ano, when the given angle is greater than 270 degrees, to look for the reference angle, we subtract the given angle from 360. So 360 minus the standard angle will will yield to the reference angle so when when standard angle is greater than 270 the vector is found in quadrant 4 so the description for quadrant 4 the direction is south of the east line so let us have the following example so find the direction of vector n when n is located at angle of 220 degrees so 220 so 220 is greater than 180 but 220 is less than 270. so if we go back to our table this is the situation So, yung 220 is greater, mas malaki siya kay 180, pero maliit siya kumpara kay 270. Therefore, to find the value of our reference angle, we use this equation. reference angle is equal to the given angle minus 180 so 220 degrees our given angle which is a standard angle minus 180 is equal to 40 degrees therefore the direction of our vector is 40 degrees so if we will put it in a graph so this is it so 220 that is the reference standard angle nothing with respect to one revolution so meaning little 90 degree 180 degree and then 220 degree so that so the tonight in my hand up young angle not 10 so 220 degree so we we looked for the the value of reference angle to describe the direction of vector n so since and it is a quadrant number three mahana then the direction is south of west and the value with respect to the west line the the ref the the angle created with this by this vector is 40 degrees. Therefore, N is 40 degrees south of west.

It is located 40 degrees south of the west line so for other examples we have other examples in our anyways Nasa ibang ano ata nasa kabila ata file. So dun sa module nyo madami pa dyan example. so you can familiarize yourself with it so just remember this rule if the angle you gave is an angle with respect to the 360 degree so how will you know that with respect to the 360 degree or panino malala man a standard angle and given sign you condition of BB gain on iron non north of east non location yeah quadrants so this is a BB vehicle north of East Basha north of West south of West or south of East yeah so you know rules so you know you know you condition and these are the equations for that rule so let's discuss the magnitude of a vector so vector has a magnitude and if a magnitude is given we write it using a light-faced letter or the symbol of vector enclosed in vertical bar so kanina pinakita ko na yan sa iyo so if the numerical value is given we write write the value so this is the symbol of the magnitude representation of the magnitude of a vector excuse me and then yes example so So vector n is n 40 degrees south of west. So this is the quantity.

This is the value of the vector. So when we say magnitude of a vector, it talks about the length of the vector. so that length can be measured in different with different units can be associated with different units so kapag naman daw number numerical value ang binigay then we replace the letter with the numerical value so for example vector n is 25 kilometers 40 degrees south of west so the length of the vector the magnitude of a vector is the length the measure of the length of a vector so if a vector is to scale we can measure the actual magnitude of that vector using a measuring device so for example if one kilometer so if one kilometer is scaled to one centimeter then in a ruler every one centimeter is equivalent to one kilometer so kapag kapag ang vector mo is two centimeters long ibig sabihin sa totoong ano in real situation so in real situation that corresponds to two kilometers so so you can also use other units here so for example one newton a one centimeter is equivalent to one newton so in and then For example, we have an arrow. that is four centimeters long so it means if you measure the arrow using a ruler and then four centimeters long then that means that our arrow is four kilometers in real life so right if in real life We are not drawing, we are not measuring the 1 kilometer in the bond paper for example. So this concept is also used in maps for example here.

So we have scales. So for example this. So every graduation this means that this is equivalent to kilometers if you measure it it is equivalent to kilometers the same with this one the scale in our map so here, every 1 cm our scale is 1 cm is to 1 km so meaning, every 1 cm in our ruler is equivalent to 1 km so it can be every 1.5 cm or every 0.5 cm is equivalent to one kilometer so you can decide how you want to scale your measurements so there are different types so four types of vectors first is the equal vectors equal vectors are when two vector i saw so two vectors are equal if they have the same magnitude and direction so in in graphical representation so the direction of the vectors are pointing so that the vectors are pointing towards the same direction so equal yung direction and the same direction and then the same din yung magnitude so ito 4 kilometers Vector A and Vector B are pointing towards the east side.

Therefore, Vector N and Vector B are equal. They can also be equal but pointing towards the north. So, they should be in the same direction and the same magnitude.

The second type of vector is the parallel vector. So, two vectors are parallel. if they have the same direction but may have different magnitude so they are pointing towards the same direction but one is longer and the other is shorter for example vector a is three kilometers towards east then b vector b is four kilometers towards the east so they are parallel vectors since they are pointing towards in the same direction anti-parallel vectors if they have an angle between if the angle between the vectors is but bucket one thousand times 180 degrees degrees da pato if the angle between the vectors is 180 degrees or if they are pointing towards the polar opposite of each others for example it only suck it don't miss up is pointing towards the West while the other one is pointing towards the east so this is also an example of anti-parallel so or you miss up pointing towards the north you miss up pointing towards the south or further in the manual so further in the manner ganyan so you miss a pointing towards the south of west is a pointing towards the north of east so these are anti-parallel vectors and the last type of vector is so before we go to the last type of vector so equal vectors parallel vectors and anti-parallel vectors are collinear vectors so it means the vectors lie in the same line of action for example This is the line of action. So, they are both horizontal.

Or they are both diagonal. They are both vertical vectors. So, the last type of vector is the non-collinear vector.

So, two vectors are non-collinear if they are on the same plane but not acting on the same line of action. So these vectors are separated by an angle that is not equal to 0 and not equal to 180 degrees. so for example is the right vectors divided separated by 90 degree angle so you miss up pointing towards the north you miss a number pointing towards the east or putting kites and direction as long as right angle so any vector separated by a right angle or nine separated by 90 degrees or non-collinear vectors so any vectors that are perpendicular to each other are non-collinear vectors so any acute any vectors um divided or separated by an acute angle so if we say acute angle those are angles that are less than 90 degrees for example 45 89 and below so that but not equal to zero so acute angle vectors that are separated by an acute angle is a non-collinear vectors and the same with the obtuse with obtuse angles so two vectors separated by an obtuse angle so kapag obtuse those are angles that are greater than 90 degrees so 91 92 93 94 but not equal to 180 degrees so any two vectors separated by an obtuse angle is a non-collinear so that is all for this part two of vectors so in our next video we're going to discuss vector addition and then representing vectors in component form so paano tayo mag-a-add ng vectors adding two vectors or adding two or more vectors and how do we use the different methods of vector addition so thank you for listening

Transcript for:Physics Vectors Overview

Transcript for:
Physics Vectors Overview