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### Cross product

The **cross product** is an operation in the three-dimensional Euclidean vector space that assigns a vector to two other vectors.

##### Explanation

The name *cross product* is derived from the cross "**×**" that is often used to designate this operation; the alternative name **vector product** emphasizes that the result is a vector.

##### Example 1

The **skew product** of two Euclidean vectors *a* and *b* is

a × b= ||a|| ||b|| sin (θ)n

where *θ* is the angle between the vectors, and ||*a*|| and ||*b*|| are the norms of the vectors and *a* and *b*. The *n* is a unit vector perpendicular to the plane containing *a* and *b*, in the direction given by the right-hand rule.

## HistoryThe expression |