Verify That the Points Are the Vertices of a Parallelogram $A ( 2,2,2 ) , B ( 3,4,5 ) , C ( 7,6,3 ) , D ( 8,8,6 )$

Multiple Choice

Verify that the points are the vertices of a parallelogram. $A ( 2,2,2 ) , B ( 3,4,5 ) , C ( 7,6,3 ) , D ( 8,8,6 )$

A) $\overrightarrow { A B } = ( 1,2,3 )$ is parallel to $\overrightarrow { C D } = ( 1,2,3 )$
$\overrightarrow { B D } = ( 1,4,5 )$ is parallel to $\overrightarrow { A C } = ( 1,4,5 )$
Opposites are parallel and same length. So $A B C D$ form a parallelogram.
B) $\overrightarrow { A B } = ( 1,2,3 )$ is parallel to $\overrightarrow { C D } = ( 5,4,1 )$
$\overrightarrow { B D } = ( 5,4,1 )$ is parallel to $\overrightarrow { A C } = ( 1,2,3 )$
Opposites are parallel and same length. So $A B C D$ form a parallelogram.
C) $\overrightarrow { A B } = ( 1,2,3 )$ is not parallel to $\overrightarrow { C D } = ( 1,2,3 )$
$\overrightarrow { B D } = ( 5,4,1 )$ is not parallel to $\overrightarrow { A C } = ( 5,4,1 )$
Opposites are not parallel and same length. So $A B C D$ form a parallelogram.
D) $\overrightarrow { A B } = ( 1,2,3 )$ is perpendicular to $\overrightarrow { C D } = ( 1,2,3 )$
$\overrightarrow { B D } = ( 5,4,1 )$ is perpendicular to $\overrightarrow { A C } = ( 5,4,1 )$
Opposites are perpendicular and same length. So $A B C D$ form a parallelogram .
E) $\overrightarrow { A B } = ( 1,2,3 )$ is parallel to $\overrightarrow { C D } = ( 1,2,3 )$
$\overrightarrow { B D } = ( 5,4,1 )$ is parallel to $\overrightarrow { A C } = ( 5,4,1 )$
Opposites are parallel and same length. So $A B C D$ form a parallelogram.