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Suppose three vectors
and in three dimensional space are given so that they do not lie in the same plane. These three vectors form three edges of a parallelepiped. The volume of this parallelepiped ( is the product of area of the base and altitude ) is equal to the scalar triple product
.
It can be shown that the volume of the parallelepiped is the absolute value of the determinant of the following matrix:

.

**Subsections**

Ali A. Daddel
2000-09-15