Thread: Question about Vectors

If A(-1,3,4), B(4,6,3), C(-2,1,1) and D are the verticies of a parallelogram, find all the possible coordinates for the point D.

So I let D be (x,y,z), then I worked out vectors AB,AC,AD,BC,BD,CD and after this I don't know what to do. (am i even doing it right?) Can someone help me with this question?

Diagonals of a parallelogram bisect each other.

So,

the ans by alex is very much correct

This is what i have done so far. If vector AB is parallel to CD then x=4,y=5,z=0.

If BC is parallel to AD then x=-6,y=-1,z=2

Diagonals of a parallelogram bisect each other (BC and AC)



and i get the solution x=-6,y=-1,z=2, which is the same as my 2nd solution set.

The problem is I need the third solution set. How do I do this?

bump?