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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 (θn

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.

 


History

The expression vector product first appeared in an 1878 publication by the English mathematician William Clifford.


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