High Quality Content by WIKIPEDIA articles! In vector calculus, there are two ways of multiplying three vectors together, to make a triple product of vectors.The scalar triple product (also called mixed product) is defined as the dot product of one of the vectors with the cross product of the other two. In geometric algebra it is replaced by the 3-fold exterior product, and yields a 3-vector: mathbf u wedge mathbf v wedge mathbf w; in 3 dimensions a 3-vector is a pseudoscalar, which in the presence of a volume form is a scalar, just as in vector algebra.The parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a vector and a scalar, which is not defined.

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