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Copy the vectors in the figure and use them to draw the following vectors.

(a) $ u + v $

(b) $ u + w $

(c) $ v + w $

(d) $ u - v $

(e) $ v + u + w $

(f) $ u - w - v $

a) figure not available

b) figure not available

c) figure not available

d) figure not available

e) figure not available

f) figure not available

Vectors

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Harvey Mudd College

University of Nottingham

Idaho State University

Boston College

in this problem. It is asked to copy the vectors in the figure and use them to draw the following vectors. So here are the vectors given to us in this way. Right, So these are the three factors. Alright, So here you is here, right? We have made here. Right. And finally we are having this uh we and uselessly. Right. So we have just taken this mistakes like vectors. Okay, And just we are putting in this way. Right? So we know that a vector has been following the uh step, right, this is in you then. We this has some direction. Right? This is some direction. This has some directions, right? And the final direction will be opposed to it. Right? This is opposite, right. This is not going in this direction, right, It is going in this direction. Okay, so this is this is the common observation, we we just observe and the factors. Right? So here we can say uh here. Now for the second part we can see we are asked to find you please. W so this is also very simple, we will put just you and we allow uh sorry, you and w with it. Right, So this is also following uh direction. Right? And the opposite A deposit direction will be having from initial point to the final point. Right, So this was an initial point in the previous problem. Right, And this is our final point. So the direction will be opposite, remember. Right, so this is your place. W we have got All right, so moving ahead we will see for we plus W Right, so now here we we is given to us. Where is we? Yes, this is Director. Right? We and we can draw it as it is and you place W. Right, so w is in downward, so we will just uh yeah, we will just take a tail. You can say this is I suppose this is a fact. Right? Let us see. So the sustain and this is alright, this should be head. I'm sorry, they should be head and this is jane. Yeah. Right, so the uh you can say this, this becomes very easy. So I'll tell you. So this headed of this head is towards upright for me. So now, so from the head of the v detail of the W should start. Right? So this will go in this way. So this is the direction. Right? And the final direction will be opposed to both of them. So we can see this is this is our presentation. We are getting people's W here as a resultant factor. All right, so now moving ahead, we want to calculate the humanist humanness. We So this is also very simple, we isn't it wasn't a proper direction and we know that in the vectors if we if we draw or if we change the direction opposite to it. Right? So it becomes minus, we sign also changes. Right? So this becomes minus we and this is how we make the uh direction, party, final resultant vector. Right? So this is a final resented resulting back that. Right, okay, so now moving ahead we want to calculate for you plus V plus w. Right, so we have drawn you plus Vdo and we have drawn here on W. Right, so this should this will not make any triangle, right? Because there are three vectors to be, it is making up quadri later. So this was the initial point, let us say you plus weekend Britain as we plus you? Yes, so yes, we have a common value here and the destination point was this? So this is a final vector, this is useless, we blister Bolivia. Okay, so this is very simple, this is you place me right, this is headed headed towards this, uh the head or head of the, you can see you write and the tail of free, you can say right, okay, Mhm. So now moving forward, we are asked to find out u minus b minus u minus the blue minus v here, So this is for sure, there will be four points here. Right? So here it will be you and -5 is nothing. But this is drawn opposite to the given direction, it was downwards in the given direction if we just inverted. Right? So uh we can make it on the upper up direction and it will be minus W. Right, similarly for minus, we we have already discussed above, so this will be minus, we write and the resultant factor will be From initial .2 final point. Right, so what is our initial point? Initial point is nothing but the tail of the tale of the you went to and head of the you can see a head of the minus move back. So this is how we calculate the u minus U minus w minus week. So this is how we calculate this vector. I hope you understand the concept. Thank you for watching.