Question

Does anyone know how to draw a diagram? If →u and →v are the vectors below, find the vector →w whose tail is at the point halfway from the tip of →v to the tip of →u+→v and whose head is at the point halfway from the tip of →u to the tip of →v.

u= { 3 1 1 }
v = { 1 5 -3}

Answer 1

I'm not sure that a diagram would aid you too much here. Let's try and find what the components of w are.

\[u + v = <4, 6, -2> \]
Find the midpoint from v to u+v. Then, find the mid point from u to v.

Answer 2

Alright. However, I would assume the diagram would be more helpful.

In that case, the mp from v to u+v would be v + (u+v)

Answer 3

(v + [u+v] )/2

Answer 4

Right. The reason I don't think that a diagram would be helpful is because the persepctive of one vector appeared like a point. Once you calculate both midpoints, find the vector between them, which would be w.

Answer 5

alright,. So i calculated both w and the mp from u to v : they are correspodning to W and P:
W= ( 5/2, 11/2, -5/2)
P= (2 3, -1}

Answer 6

Is that what you got by anychance?

Answer 7

What you have labeled W is not the w we are looking for, but that is the correct midpoint from v to u+v. Your other midpoint is correct as well. Now find the vector between them and that will be w.

Answer 8

Alright, so overall, i got [1/2, 5/2, -3/2]

Answer 9

I believe that's correct.

Answer 10

nice, let me check the software!

Answer 11

Well, it looks like it is wrong: Correct answer is [-1.2, -5/2, 3/2]. This could be fixed by arithmetic and careless addition. Thank you very much for your help and guidance @RBauer4 !

Answer 12

1/2*

Answer 13

Oh, my apologies. Yes, it's basically the same vector, just not in the right direction. Your welcome and what's important is that you understand the concepts. Good luck.