# Altitude of a perallelepiped

Find the altitude of a parallelepiped determined by vectors A, B, and C if the base is taken to be the parallelogram determined by A and B and

A=i+j+k

B=2i+4j-k

C=i+j+3k.

https://brainmass.com/math/geometry-and-topology/altitude-perallelepiped-340069

#### Solution Preview

The altitude of such a parallelepiped is precisely the length of the orthogonal projection of C onto the cross-product of A and B.

It can be readily seen from a picture. The cross-product A X B is perpendicular to both A and B, and if we project C onto it, ...

#### Solution Summary

The altitude of a parallelepiped determined by three vectors is calculated.

$2.19