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 u−v. Assume all vectors are in standard position.
u: (-2,3,-1) v: (4,3,5)

Question

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 u−v. Assume all vectors are in standard position.
u: (-2,3,-1) v: (4,3,5)

kc_kennylau · Answer

Find u+v and u-v first?

kc_kennylau · Answer

Halfway is divided by 2

anonymous · Answer

Find u+v then find the midpoint between the tip of v and the tip of u+v.  That is where the tail is.

anonymous · Answer

Find u-v then find the midpoint between the tip of u and the tip of u-v.  That is where the head is.

anonymous · Answer

Standard position means tails at the origin (original vectors u and v).

anonymous · Answer

Ok, that sounds right

anonymous · Answer

But I don't think that you're done yet, as you would have a vector PQ but you would need to translate it to standard position.

anonymous · Answer

Do do that just put vector W = PQ into component form and subtract the components <q1-p1,q2-p2,q3-p3> = W in std. position

anonymous · Answer

Q being the tip, P being the tail.

anonymous · Answer

w= -7,-3,-8

anonymous · Answer

Spot on mathbrz, thanks!

anonymous · Answer

Awesome, glad to help!