< 1 >
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 vector product first appeared in an 1878 publication by the English mathematician William Clifford. |