# Volume of a parallelepiped and vectors

A parallelepiped is defined by the three non-collinear vectors A, B, C. Show that the enclosed volume is given plus or minus the triple scalar product (depending on whether the product contains the vectors in cyclic or anticyclic order).

© BrainMass Inc. brainmass.com June 3, 2020, 6:30 pm ad1c9bdddfhttps://brainmass.com/physics/right-hand-rule/volume-parallelepiped-vectors-62570

#### Solution Preview

Please see the attached file.

The triple scalar product of three vectors is defined as:

This determinant is positive if the three ...

#### Solution Summary

This provides an example of working with the volume of a parallelepiped.

$2.19