# Vector product

From Encyclopedia of Mathematics

*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.

#### Comments

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: http://encyclopediaofmath.org/index.php?title=Vector_product&oldid=13392

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article