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

question 132

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.

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