Vectors and Lines - Confirmation

vg19

Hey,

I just would like confirmation on this question.
A parallelogram has sides A,B, BC, CD, DA. Given A(1,-1,2), C(2,1,0) and the midpoint M(1,0,-3) of AB, find BD(vector).

This is what I did. To find point B, I used the midpoint formula

(1,0,-3) = 1/2[(x+1), (-1+y), (2+z)]

Solving that, I got B as (1,1,-8)

I then found AB = (1,1,-8) - (1,-1,2) = (0,2,-10)

I then found D by saying (2,1,0) - (0,2,-10) = (2,-1,10)

Finally BD = (2,-1,10) - (1,1,-8) = (1,-2,18)

Im not sure if I did this correctly of even if my method at all was correct. Any confirmation would be much apprecieated.

mathmike

looks good to me