Vector product

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of a vector by a vector in

The vector , denoted by the symbol or , satisfying the following requirements:

1) the length of is equal to the product of the lengths of the vectors and by the sine of the angle between them, i.e.

2) is orthogonal to both and ;

3) the orientation of the vector triple is the same as that of the (standard) triple of basis vectors. See Vector algebra.


If have coordinates and with respect to an orthonormal basis in , then the coordinates of are .

How to Cite This Entry:
Vector product. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article