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I'm reading about a way to solve for the volume of a "parallelepiped" in 3 space, which is determined by vectors u, v and w. The volume is apparently the absolute value of the determinant given by the matrix

u1 u2 u3

v1 v2 v3

w1 w2 w3

which is the same as the scalar triple product given by: u . (v x w)

My question is, the cross product of two vectors is not communitive. v x w

does not equal w x v.

Yet, the vectors for a parallelepiped could be given in any order. How do I know how to set up the matrix for an object like this, as it will affect the volume?

Thanks!

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# Scalar triple product, volume, and ordering

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