Find the volume of the parallelepiped with the given vertices
$A ( 0,0,0 ) , B ( 2,0,0 ) , C ( 0,3,0 ) , D ( 2,3,0 ) , E ( 0,0,5 ) , F ( 2,0,5 ) , G ( 0,3,5 ) , H ( 2,3,5 )$ .

A)15
B)30
C)7.5
D)60
E)120

Question

Find the volume of the parallelepiped with the given vertices 
 $A ( 0,0,0 ) , B ( 2,0,0 ) , C ( 0,3,0 ) , D ( 2,3,0 ) , E ( 0,0,5 ) , F ( 2,0,5 ) , G ( 0,3,5 ) , H ( 2,3,5 )$ .

A)15
B)30
C)7.5
D)60
E)120

Quizplus · Accepted Answer

The volume of a parallelepiped is given by the scalar triple product of its edge vectors. Here, the vectors are $ \vec{AB} = (2,0,0) $, $ \vec{AC} = (0,3,0) $, and $ \vec{AE} = (0,0,5) $. The volume is $ | \vec{AB} \cdot (\vec{AC} \times \vec{AE}) | = | (2,0,0) \cdot (0,0,15) | = 30 $.