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jesshuifeng

What is the use of knowing the volume of a parallel hexahedron composed of these vectors?

seven

If we reverse the order of the cross product, we get the signed volume of the parallelepiped reflected across the plane spanned by the two vectors in the cross product.

bravech

If we reverse the order, we get the same volume magnitude but it is reflected and negative

annddrrea

We got the vector in reversed direction but same magnitude.

jiaruiz

The direction will be reversed