So I am stuck on this question it states that:
if u and v are 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. Assume all vectors are in standard position.
u = [-2,1,-5] v = [2,-2,-2]
I did the calculation and u - v = [-4, 3, -3]
But I'm not sure what the vector w is going to be.
The point halfway from the tip of v to the tip of u is
$$P=\frac{u+v}{2}=\left(0,-\frac12,-\frac72\right)$$
The point halfway from the tip of u to the tip of u-v is
$$Q=\frac{u+u-v}{2}=\left(-3,2,-4\right)$$
Thus
$$w=Q-P=\left(-3,\frac52,-\frac12\right)$$