hey gr 10 this is your favorite uncle well it is time to look at vectors and scalers if you have not subscribed uh please just make sure that you are part of this family and of course uh your favorite uncle will always bring you some good content So today we're going to look at uh vectors and scalers if you are having any challenges with your mathematics or your physical science please hop on to our website which is www. L in.co Za uh you can get all the details on the description of this video but let's get into our vectors and scalers now by definition when we talk about vectors so we're talking about um physical quantities that can be measured in terms of Direction well first magnitude right as well as dire so a vector quantity has both magnitude and Direction all right now I'm going to make an example of that right so if you think about Force so Force you can determine how large a force is as say for instance when you are pushing an object right you can determine the amount of force that you're going to apply but not only that you can also determine the direction to which you apply the force you can either decide to pull the object right towards you or you can push it away from you so force would be a typical example of a vector quantity right now what else would be a um you know an example of a vector quantity well what about weight okay so if you think about weight when we talk about weight we know that weight is also a force and it always acts vertically downwards right towards the center of the earth so it is a vector quantity well we also have velocity so I've given you three examples I said one would be Force right so force is an example of a vector quantity and the second one we set the weight of an object we know it acts vertically downwards or towards the center of the earth well weight is another type of force as well but um what about velocity as well okay so the velocity of an object so usually when we talk about velocity we want to know in a straight line where an object it is moving towards but we also want to know the direction of that object okay right now the difference now or in this case the adversary to a vector quantity is a scalar quantity right so now what are scalar quantities these are physical quantities that can be measured only in terms of magnitude so scalers can be magn can be measured in magnitude only all right now think about it what are examples of scalar quantity there's one that we always use time right well you can't say time went to the left or to the right okay it would be somewhat ridiculous to say that okay so time is an example of a scalar quantity right but what other examples are there for scalar quantities right you talk about distance right now if you think about distance distance is simply you know you can go around and around and around and around we are not concerned about Direction but in this case we just want to know the total path length that someone has moved right so in this case we know that that is an example of a scalar quantity well I want you to think what other examples are there of scalar quantities right okay so you you can think of many now I want us to take a couple of examples I want you to tell me firstly what do you think about heat is it a vector or a scalar quantity well I guess you would know that it should be a scalar quantity right the amount of heat in this case does not have Direction okay what about weight okay I've said that one okay we know that weight would be a vector quantity right so weight is a vector Quant quantity well another example what about the mass of an object would it be a scalar or a vector quantity of course this would be a scalar quantity okay because in that case when we talk about the mass right um the mass of an object is is the amount of matter that it has right so in this case we would say that is a scalar quantity of course we can talk about and many other types uh of quantities if you think about energy right so if you say uh perhaps uh eat some food and you've got a lot of energy right so in this case what can we say well energy is definitely a scalar quantity right uh because we can only quantify it in terms of magnitude and what about uh in this case if we talk about um the the momentum of an object of course we're going to still talk about momentum a little bit later so in this case momentum um when we talk about momentum this is the product of mass and velocity and as a result it will be a vector quantity right and I want you to think of so many others right that you can think of that are vector quantities right by the end of this video we should be um we should be able or in a position uh to tell the difference between number one uh scalers and vectors number two we should be able to represent those vectors using arrows so that's what we're going to do right in the next few minutes right and of course we should be able to add vectors now let's try and represent uh vectors in this case so if we want to know how to represent vectors okay so representing vectors so if we want to know how to uh represent those vectors what do we do right so remember we said every time that we represent a vector quantity we are going to show its magnitude and its direction now the first thing that I want you guys to always remember when we represent a vector we use a line okay and the length of that line would show us the magnitude okay so length equals magnitude so if I've got two forces right and let's say the one force is 50 Newtons and the other force is 30 Newtons when I draw the vector diagrams for those two forces the one that is 50 Newtons should be to should have a longer length of line than the one perhaps that is a uh that is 30 Newtons right now what we do is we draw those lines to scale and I'm going to show you how to choose a scale uh in this case right so now we know that the length of the line shows us the magnitude and then we use an arrow okay now for the arrow Arrow the arrow shows us the direction of that force all right now please I want you to note in this case right that the uh where the arrow is heading would be the direction of that Force so I'm going to show you in just a few in this case on how we go about doing that so if I said to you we are applying a force let's say of 50 Newtons um to the left or you can say towards the east so what I'm going to do is just show there with the head of an arrow right we call this the head and we call this the tail okay that's going to be important of course uh let's say the 50 Newton um force was to the left um so this is how we would show it if the 30 Newton force was to the right say for instance we're going to show it like that now you can tell by the size of those lines uh that first of all they are two different um magnitudes that we have but as well as two different directions okay right so what I want us to do right now ladies and gents is just to take an example where we are going to take um you know the vector uh diagram for a force right so if we were pulling something or if we we uh we are pushing something right and ultimately we are now going to take now let's talk about this word resultant okay so what would be the resultant of forces right so we say that the resultant of forces is a single force or resultant Vector right uh it is a single vector that has the same effect that has the same effect uh the same effect all right let's write that down as all the vectors combined all right so this is very important because now which means whenever I've got a combination of forces right I can represent them as one single Force right in this case that single force would be simply called the resultant all right now let's take an example and let's see how to draw one let's take our very first example so we've got they so they say to us show The Following vectors using Vector diagrams they say a force F1 of 50 Newtons is pulling to the right now please I want you to note ladies and gents there are several things that are important to us now the first thing that we're going to do is to choose a scale right so uh you must always make sure that you choose a suitable scale okay so let's do this I'm going to choose a scale I'm going to say 1 cm n it's going to be too small let me say 2 cm equals to 10 Newtons okay so meaning on my ruler I'm going to show you just now on my ruler right I am going to choose 2 cm and that will be the size of 10 Newtons now I'm drawing a force of uh fub1 right that is pulling to the right of 50 Newtons so I want you to note what you do with your scale you can say well if 2 cm is equal to 10 C uh 10 Newtons then how many cm will be equal to 50 okay so you can actually do it like that and what you do is you cross multiplied look at this the Newtons are on one side the ctim are on one side right so you can cross multiply there and say well 10 * X will give me 10 x and 50 * 2 will give me 100 so which means in this case I'm going to divide both sides by 10 all right and which means the amount of CM that I need to have would be 10 cm for one uh I mean for 50 Newtons all right now let's try and draw that okay so our answer answer so note this is a CM from here okay and that's that's 20 okay it's 10 that's 20 so remember we said 2 cm rather uh um I meant 2 cm that's 10 Newtons right so that's going to be okay right there we go so if you note there that would be 10 Newtons 20 newtons 30 Newtons 40 Newtons and 50 Newtons right so uh please uh don't include the dots I was just showing it to you that I've taken 2 cm to represent one dot okay to represent 10 Newtons rather so all I need to do now is to place my arrow okay so that you can see where my Vector is going so remember we said that is the tail of our diagram and that uh the tail and this is the head of our diagram so that is the answer to question one we wanted a force of 50 Newtons pulling to the right and then um two we said now we are looking for a force of F2 all right so please let's label this Force so we need to definitely label the force so this would be fub1 right so which is 50 Newtons to the right and please uh don't forget to label your forces right now let's go to the next one we said all right for the next question we are now looking for a force of F2 that is 20 Newtons right so you can check again and say well if your scale says 2 cm is 10 Newtons then how many cm will be equal to um 20 I'm sure you can already see this by now uh that it will be twice as much right so in this case you can say 10 * X this will give me 10 x right if you cross multiply there and you say 2 multiplied by 20 this will give me 40 and so if I divide both sides by 10 in this case what I do get is X is equal to 4 cm right so now let's draw that diagram for ourselves okay so I'm going to say well that's one 2 three and four right so just to be on the safe side of accuracy right so this would be the tail end right and in this case it means I'm going to place my arrow over there right so that is how our Vector diagram is going to look like this is the force FS2 this is equal to 20 newtons and we had said it must be to the left okay so now there is our F2 Force now let's go for the next one if we took right they say we must draw the force of minus fub1 so which means we want the negative of fub1 now remember that in this case in vectors when ever you've got a negative what it means is that it's a force in the opposite direction now originally where was fub1 going right FS1 was pointing to the right and so which means minus FS1 would be in the opposite direction so this would be to the left so let's take minus F1 remember we are still keeping to the same scale so which means that I am going to have 10 10 cm okay so minus fub1 that's 1 2 3 4 5 6 7 8 9 and 10 okay I'm going to stop right there right so this would be minus fub1 meaning that the head would be pointing to that side so that would be the tail so this is the force minus fub1 which is equal to 50 Newtons you can see clearly right uh it's magnitude as well as its direction right now let's go on to the next one they wanted us to calculate or to find 2 F2 so which means 2 * the amount of F2 so 2 * What's the magnitude of our F2 it is 20 Newt so 2 * FS2 so 2 * 20 newtons this should be 40 Newtons now they didn't say anything about the change in Direction meaning that we're going to still maintain the same direction the only difference now is that we are going to have a force rather that is in um uh that is that is 40 Newtons now note in this case if 20 newtons was 4 cm then it means that 20 40 Newtons would be 8 cm but again what you can do is just use your calculations right you can say well if 2 cm gives me 10 Newtons right so how many cm would give me 40 Newtons okay so cross multiply there we've got uh x * 10 this would be 10 x and 2 * 40 this would give me 80 and so if I divide by 10 again on on both sides so in this case the value of x would be 8 cm right so in this case it means that I'm going to draw a force of 8 cm right and it must be to the left remember that our F2 was to the left so in this case let's do that okay let me just use a different color so 1 2 3 4 5 6 7 and 8 so that is going to be 8 new uh 8 cm and in that case that is the equivalent of uh that is the equivalent of 40 Newtons of a force so remember we said we need to label so this would be 2 F2 which is equal to uh 40 Newtons right we're still maintaining the same direction it is to the left now ladies and gents finally we said well um what if we want the resultant of the force so this is very very important ladies and gents right so what do we do when we need to calculate the resultant of a force right so firstly we've already chosen a scale that's the first thing we need to do right now what we are going to do is we are going to use what we call a head to tail Method All right so the head to tail method so we're going to use the head to tail method now in the head to tail method what you're going to do is a you are going to draw the one vector so draw the first Vector okay now the second thing that you're going to do is then draw the second Vector uh draw the tail of the second Vector in the head of the first so draw second vector or let's rather say draw the tail of your second Vector in the head of your first right all right now let's see how to go about doing this now we are combining vector fub1 and FS2 you remember we said that fub1 was 50 Newtons to the right okay so I'm going to start with Vector F1 if you don't mind right so I'm going to say right remember we've got fub1 okay want us to uh draw that Vector so remember we said our F1 remember when when we drew it we said Vector fub1 was 10 cm right so I'm going to draw 10 cm Force okay so there we go one two 3 4 5 6 7 8 9 and 10 so there we've got F1 over there right it starts there and ends uh at at that point so remember we said Vector F1 goes to the right so this is the tail this is the head so we place an arrow there at the head of the arrow right then at the head of the first Vector right that's what we said draw the second Vector right at the head of the first Vector right so actually this this was supposed to be at okay right so now what I'm going to do going to say right so I know my first Vector ended over here all right so now my second Vector which is FS2 right remember what was the size of FS2 FS2 was uh where is our FS2 was 20 newtons to the left right so I'm going to draw a vector there which is 20 new to the left so remember we said our 20 newtons so I'm starting at the head of the first Vector okay there we go it's 20 newtons so it should end right over there remember it was 4 cm right so there is our Vector FS2 so now our Vector F2 ends over there so we want to get the resultant okay now to measure the resultant of this Vector we are going to now take the from the we measure from the head right or rather from the tail of the first Vector to the head of the second Vector from the tail of the second to the head of the first Vector now remember this is going to be the tail of our first Vector I'm going to measure from there of course you're going to have this a little bit more neatly uh than I did all right I'm just trying to make sure that I get this right all right there we go so there is my Vector right so from the head of the first to the tail uh rather from the tail of the first to the head of the second Vector so there is my Vector my resultant so this is the resultant so what we can do is measure that resultant okay so when I measure that resultant note it is one okay I want to show it there it is 1 2 3 4 5 and six right so it's 6 cm so in this case what would be the amount in the this case in terms of resultant so remember we said well 2 cm is equal to 10 Newtons right now how much will 6 cm give us well it will be an x amount so let's cross multiply again right so we're going to say 2 * X gives me 2X and 6 * 10 gives me 60 and if I divide both sides by two x will be equal to 30 so that means that for my Vector my resultant is actually going to be 30 Newtons now of course there is another way in which we could uh find that value let me just quickly show you in terms of uh the calculation we know that Vector fub1 was 50 Newtons to the right we knew that Vector FS2 was 20 newtons to the left right so in this case I want you to note if we choose a positive direction if we choose to say the direction to the right is our positive direction direction right so in this case what this simply means is that fub1 will be equal to 50 Newtons then it means FS2 will be equal to minus 20 newtons so what we do to calculate vectors in one dimension we simply say Well it means that the resultant will be equal to fub1 plus minus FS2 remember that we said NE uh FS2 is actually in the opposite direction or we can simply say fub1 + FS2 actually we put the minus when we are substituting right so this will be fub1 1 so note it will be 50 Newtons plus a -20 okay and so if you look at that mathematically that will be 50 - 20 and that will give me 30 Newtons note my 30 Newtons is positive and what is it signaling to me that it must be in the direction of my posi postive uh choice that is to the right so it's 30 Newtons to the right so this is how we are going to obtain it using um uh calculations and this is how we are going to obtain it using Vector diagrams okay right so that is how we are going to do Vector diagrams ladies and gents please just check us out again right we're going to be taking this a little bit further and just looking at um in this case uh Motion in one dimension and of course as I did say if you are still struggling with vectors uh you're are more than welcome to um get in touch with us all the details that you need will be on the description of this video otherwise ladies and gents that is how we are going to leave it uh today right uh we will come back with the next one from me for now I'll see you next time shop shop