Thread: Missing apex on a parallelogram

Let A=(1,0,-2), B=(-1,1,2),C=(3,4,0)

(a) Find the point D such that ABCD is a parallelogram where the apex D is opposite to A.

(b) Write parametric equations and symmetric equations of the line L passing through D and parallel to the segment BC.

Hello, Undefdisfigure!

Let: .

(a) Find point such that is a parallelogram where vertex is opposite

We would find vector like this . . .

. .


Let
We know that: .


We would find vector CD like this:

. .

So we have: .


Therefore: .

(b) Write parametric equations and symmetric equations of the line
passing through and parallel to the segment

The direction of is: .


The line through with direction has equations:

. . . . . . and . .