Vector and line question?

Question

I dont know how to do this question can anyone help ??

If U(5,-2,-6), V(-3,-1,2), and W(11,1,-12) are three points, find the vector X = [a,b,c]^T that has:
(i) initial point halfway between V and W;
(ii) terminal point at OU + OV (OU and OV are vectors)

a=?
b=?
c=?

Answer 1

The initial vector point coordinates are the means of corresponding coordinates of points V and W. That is
X=(4, 0, -5)

The terminal point coordinates are the summs of corresponding coordinates of U and V, thus
Y=(2, -3, -4)

Therefore the vector coordinates are (XY, i.e. Y-X)

a= -2;
b= -3;
c= 1.

Answer 2

Given three points

U(5,-2,-6), V(-3,-1,2), and W(11,1,-12)

Let M = midpoint between V and W.

M = (V + W)/2 = ((-3 + 11)/2, (-1+1)/2, (2-12)/2) = (4, 0, -5)

Let N = OU + OV

N = (5-3, -2-1, -6+2) = (2, -3, -4)

So vector X = MN = N - M = <2-4, -3-0, -4-(-5)> = <-2, -3, 1>

a = -2
b = -3
c = 1