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 and whose head is at the point halfway from the tip of u to the tip of u-v.

u = (-2,-4,-5)
v = (-3, 5, -1)

answer: (2, -7, -3/2)

Answer 1

How?

Answer 2

so, the tip of v and u are the position vectors temselves, right?

Answer 3

P = midpoint between "u" and "v"
\[P\equiv\left({-2-3\over2},{-4+5\over2},{-5-1\over2}\right)=(-5/2,1/2,-3)\]

Answer 4

Q = midpoint between "u" and "u-v"
\[u-v = \left(-2+3,-4-5,-5+1\right)=(1,-9,-4)\\
Q\equiv\left({-2+1\over2},{-4-9\over2},{-5-4\over2}\right)=(-1/2,-13/2,-9/2)\]

Answer 5

now,
\[\vec{PQ}\equiv\left({-1+5\over2},{-13-1\over2},{-9+6\over2}\right)\\
\boxed{\vec{PQ}\equiv(2,-7,-3/2)}\]

Answer 6

THANKS!

Answer 7

yw.