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Altitude of a perallelepiped

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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.

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Solution Summary

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

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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, ...

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