Question about vectors and rectangles in R3

[ericpei22]

Hi all, I was doing some review questions for my vectors test tomorrow and I have no idea how to even start this one. I hope any of you can help me

Homework Statement

The rectangle ABCD has vertices at A(-1,2,3), B(2,6,-9) and D(3,q,8).
Note that the "q" in coordinate D is a variable

a. Determine the coordinates of the vertex C
This is the question I am stuck on, no idea how to start. This question is in the dot/cross product section of the textbook, so I'm assuming we have to use either one to solve this problem

b. Determine the angle between the two diagonals of this rectangle.
Need the vertex C to figure out the diagonals...

Homework Equations

if a= (a1, a2, a3), b= (b1, b2, b3),

a.b = a1*b1 + a2*b2 + a3*b3
a.b = |a|*|b|*cosσ, where σ is the angle between a and b

The Attempt at a Solution

I found coordinate D to be (3, 14, 8) and am trying to use the fact that in this case, a.b = 0 because it is a rectangle and every side is perpendicular.

Any help is appreciated, thanks!

EDIT: Solved, I was just over-thinking it. Thanks anyways

 

[Mark44]

A comment on your use of the word "coordinate."

D is a point, not a coordinate ("I found coordinate D ... "). What you did was to find the missing coordinate of point D.