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
Is the parallelogram a rectangle? Justify your answer.
Hello,
$\displaystyle \vec{AB}=\vec{DC}$
that should give you the coordinates of D.
As to know whether it's a rectangle or not... you should know that a rectangle is a parallelogram with a right angle.
So check if the scalar product between $\displaystyle \vec{AB}$ and $\displaystyle \vec{BC}$ is 0.
Memo : $\displaystyle Ax_a,y_a,z_a) \text{ and } Bx_b,y_b,z_d) \quad \Rightarrow \quad \vec{AB}x_b-x_a,y_b-y_a,z_b-z_a)$
(coordinates of vector)