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.

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- April 27th 2009, 02:23 PMUndefdisfigureMissing 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. - April 27th 2009, 03:07 PMSoroban
Hello, Undefdisfigure!

Quote:

Let: .

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

. .

Let

We know that: .

We would find vector CD like this:

. .

So we have: .

Therefore: .

Quote:

(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 . .