Parallelogram Question

• May 24th 2009, 12:54 PM
peon123
Parallelogram Question
ABC has vertices of A(3,2,-5) B(4,-1,7) C(-8,3,-6)

Determine the coordinates of D such that ABCD is a parallelogram

• May 24th 2009, 01:18 PM
Moo
Hello,
Quote:

Originally Posted by peon123
ABC has vertices of A(3,2,-5) B(4,-1,7) C(-8,3,-6)

Determine the coordinates of D such that ABCD is a parallelogram

$\vec{AB}=\vec{DC}$
So check if the scalar product between $\vec{AB}$ and $\vec{BC}$ is 0.
Memo : $A:(x_a,y_a,z_a) \text{ and } B:(x_b,y_b,z_d) \quad \Rightarrow \quad \vec{AB}:(x_b-x_a,y_b-y_a,z_b-z_a)$