so welcome to part two of lecture two introduction of physics so in this video we're going to discuss um 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 well vectors is described by magnitude appropriate units and with direction so a mix of mean 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 so 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 uh 39 degrees celsius north or 39 degrees celsius east so it doesn't make sense so therefore temperature cannot be associated with direction the same with time so walnut one hour north one hour is the bus the same with other scalar quantities so you mix it with scalar quantities or quantities which cannot be associated with direction so description lanyard is the magnitude and the respective 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 c four so when for example we applied um 10 newtons to one side of an object so of course the direction of the of the force is to the direction to to is the same with the direction where you apply the force for example naga play cannon 10 newtons is then the direction is of the forces east so velocity in a minus when you apply direction to the speed so copper negative direction to the magnitude to the magnitude of speed then that is not the speed that becomes velocity and velocity for example um a car moving seven kilometers per hour june north so it wasn't being seventeen kilometers per hour northfield velocity yeah so again um 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 arrow head so arrowed line and then the direction of the arrow head indicates the direction of the quantity so for vector a the direction is east for vector b's direction is west s and then relative to the north east west south the line pudding direction dunya is north east northwest south east and southwest the length of the arrow is scaled to be proportional to the magnitude of the vector quantity it 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 b so meaning value 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 ito for the representing vector using a capital letter with an arrow head above or using a bold face letter control bold face you letter so that denotes a vector quantity 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 arrow head on top or the symbol of the vector placed inside a vertical bar vertical side so that symbol symbolizes the magnitude of a vector okay to represent the magnitude of a vector we can place this vector symbol within a vertical bar or we can place this bold faced letter within a vertical bar so you know representational magnitude of a vector so how do we locate or how do we um i 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 with respect to the horizontal axis so take note that the acute angles or angles less than 90 degrees so in this case for the vector the ninth the 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 i am so horizontal in x-axis not and that is the east-west line so on another acute angle nothing 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 ebox at the end the arrow is not is found north of east so this is the angle so nitinoman the the vector vector a is found north of west and then detailed the vector is found south of west and lithium and south of eastern the letter n or north and south and s out south is written after the measure of the angle followed by the place of e for east and of w for west so for example 60 degrees s of w so this is the measure of angle followed by south or direction is north then north anglage 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 quality so it makes a million 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 in sujan shamahana 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 see vector a nakita not then that it is directed north of east the direction of vector a so with respect to the east line vector a is 30 degrees north of the east line so therefore capacitor a is 30 degrees n of e while sibinoman with respect to the east-west line so since i need the semi-west line with respect to the west line vector b is 45 degrees south of west yeah so let's answer the following so let's determine the direction of the vectors a b c and d so on direction vector so you can pause this video and then go back okay so to answer this activity vector a with respect 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 long reference number nothing with respect to the west line so b is 45 degrees 45 degrees north of the west line so an answer is 45 degree n of w so cinnamon is 20 degrees south of the east line superbaba south of the east line and then d is simply south directed south so how do we you know 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 given we identify the direction then to represent it so for example given a monitor represents a 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 our long or along the east-west line so again now 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 in 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 samara and ion quadrant one quadrant two quadrant three and revolution or evolution being so one revolution or one rotation in the cartesian plane represents 360 degrees unit measurement yeah so therefore therefore if we divide it into four quadrants so each quadrant measures 90 degrees so the first quadrant is from zero to 90 degrees the second quadrant from 90 degrees to 180 degrees later pacquiao 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 also the degrees of each of the line each of this direction okay so ayanna so to use a protractor so to use a protractor and so that represents the point of origin so make sure that the the horizontal line and the the horizontal line and the vertical line aligns with your i know with the cartesian plane so if you want to measure for example 10 degrees north of east sudito so from from this side 0 degrees 10 degrees 20 degrees 30 degrees 40 50 60 70 80 90. for example so if you want to determine the angle if you want yes if you want to determine the angle then from zero degrees autonomous outer numbers labels so zero degrees this is 10 degrees this is 20 degrees 30 40 50 60. for example so make sure now numbers outer number 10 20 30 40 50 60 70 80 and then a month inner um inner calibration 10 so 10 20 30 40 56 to 70 young 90 so each of these are 90 degrees so that the 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 120 it is 60 degrees so the same with this side for example in this side for example is 40 degrees with respect to our west line so the nomencla this is that this vector is 30 degrees with respect to the west line so movement now pang b long is from the east west line so 10 20 30 and 10 20 30. okay so example so example also graphically represent vector a which is directed 30 degrees north of east so north of east is found in quadrant one so north of east sudito degrees north of east so we make use of our little i already placed a mark marking so from the east line magbilant 30 degrees so 10 20 30 degrees so again mark and then next is to connect yeah so using a ruler to scale for example for example my scale nana mehrangan ration for example for every one centimeter um i one kilometer equivalent just so one kilometers scenario then you can already you know do it so vector a which is directed 30 degrees north of east graphical representation angle created by vector a with respect to the east line so to look for to identify also or to to have an example for the other direction so other quadrants so let us look for the following and 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 sunny south so young south and this is east so quadrant number four so using a protractor hanapin attention 78 degrees so this is 10 20 from the east line milan tayo 10 20 30 40 50 60 70 and then and so each markings graduation is one degree so therefore anditos is seven to eight degrees so therefore this line so this vector now represents vector a which is 78 degrees south of east so how about it all cb is 39 degrees north of west excuse me so north of west is found nito it's the second quadrant so this is the west line north now west line and quadrant two so next is to make sure you 39 degrees so since anja then so with respect to the west lime and bilanta young 39 degrees so 10 20 30 and then 35 and then 36 37 38 39 so enjoying 39 degrees then connect the line so using a ruler yeah so to represent this um vector with its direction in a graph in a diagram direction and last vector c is 15 degrees out of west so south of west this is our west line south non-west lines so that's a quadrant three 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 little 10 11 12. okay so 10 11 12 13 14 15 degrees so this is i don't know marking those 15 degrees and then it raises you know you 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 the so how do we find the direction of vectors with angles in standard form so for example association north east southwest so hindi language the 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 is 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 before we we go to the equations for the reference angle or the formula for the parent's angle so again so review all that 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 degrees 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 zero degree to 90 degree from the north line to the west line and measure nothing 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 217 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 are 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 dependence and even situation as a given angle if our if the given standard angle is less than 90 degrees then our reference angle is equal to the standard angle is less than 90 degrees you know reference angle and the location of that of the vector is in quadrant one or in northeast north of the east line capacity 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 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 is greater than 90 but is less than 180 then the vector is found in quadrant two so on quadrant direction is north of the west [Music] is greater than 180 but less than 270 degrees then to look for the reference angle or the the value of the acute angle we use this equation 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 we're in the description is south of the west line when the 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 four so the description for quadrant four 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. therefore to find the value of our reference angle we use this equation so reference angle is equal to the given angle minus 180 so yeah so 220 degrees our given angle which is a standard angle minus 180 is equal to 40 degrees so therefore the direction of our vector is 40 degrees with respect to one revolution so meaning little 90 degree 180 degree and then 220 degree so that sodium angle nothing so 220 degree so to we we looked for the the value of reference angle to describe the direction of vector n so since anditas is a quadratic then the direction is south of west and the value with respect to the west line the the ref that 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 scenario with respect to the i know the 360 degrees so finally with respect to the 360 degree or malala standard of eastern location [Music] 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 face letter or the symbol of vector enclosed in vertical bars so nina pinakita condensate so if the numerical value is given we write the value so this is the symbol of the magnitude representation of the magnitude of a vector excuse me and then as an example so vector n is n 40 degrees south of west so this is the quantity yeah this is the the value yeah value of the vector capacitor nothing 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 kapagnam and number numerical value of mini guy 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 and 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 kilo so if one kilometer is scaled to one centimeter then in a ruler every one centimeter is equivalent to one kilometer so capac two centimeters long in real situation so in real situation that corresponds to two kilometers it's going on so so you can also use other units here so for example one newton a one centimeter is equivalent to one newton so and then yeah so for example we have an arrow that is four centimeters long so it makes a b using a ruler and then four centimeters longsha then that means that our arrow is four kilometers in real life of the drawing paper for example so this concept is also used in maps for example dito ayan so every and every graduation this means that this is equivalent to kilometers capac ministry it is equivalent to kilometers the same with this one so dito every one cm young scale nothing is one cm is to one kilometer so meaning every one centimeters in our ruler is equivalent to one kilometer so whether every one half centimeter or every 0.5 cm is equivalent to one kilometer measurement so there are different types of four types of vectors first is the equal vectors equal vectors are when two vector i sorry 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 equally equally direction in the same direction and then the same daniel magnitude so it took four kilometers vector a and four kilometers in vector b they are pointing towards the east side both of them therefore vector n vector b are equal so father man's lung equals pointing towards the north stop at the same direction in the same magnitude the second type of vector r 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 for example vector is three kilometers towards east then b vector b is four kilometers towards the east so they are parallel vector since they are pointing towards in the same direction antiparallel vectors if they have an angle between if the angle between the vectors is back at 1000 times so 180 degrees so degrees if the angle between the vectors is 180 degrees or if they are pointing towards the polar opposite of each other for example is pointing towards the west while the other one is pointing towards the east so this is also an example of antiparallel or yogis are pointing towards the north and disappointing towards the south pointing towards the south of west disappointing towards the northeast so these are anti-parallel vectors and the last type of vector is ah so before we go to the last type of vector so equal vectors parallel vectors and antiparallel vectors are collinear 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 separated by an angle that is not equal to zero and not equal to 180 degrees so for example is the right vectors divide separated by 90 degree angle so you miss up pointing towards the north yung san aman pointing towards the east orbiting kaizen direction as long as right angle so any vector separated by a right angle or 9 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 divided or separated by an acute angle so pakistan have been at an acute angle those are angles that are less than 90 degrees for example 45 89 and below so but not equal to zero so acute angle vectors that are separated by an acute angle is in an non-collinear vectors and the same with the objects with obtuse angles so two vectors separated by an obtuse angle so those are angles that are greater than 90 degrees so 91 92 93 94 but not equal to 180 degrees zero so any two vectors separated by an object angle is a non-collinear vectors 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 vectors adding two vectors or adding two or more vectors and how do we um use the different methods of vector addition so thank you for listening