# Math Help - Parallelogram Question

1. ## 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

Is the parallelogram a rectangle? Justify your answer.

2. Hello,
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

Is the parallelogram a rectangle? Justify your answer.
$\vec{AB}=\vec{DC}$

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 $\vec{AB}$ and $\vec{BC}$ is 0.

Memo : $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)" alt="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)