Cross Product

Cross Product

A way of multiplying two vectors, written u × v, in which the product is another vector. The cross product of two vectors results in a vector which is orthogonal to both the vectors being multiplied. The magnitude of the cross product of two vectors is found by the formula |u × v| = |u| |v| sin θ, where θ is the smaller angle between the vectors.

Note: Cross products are not commutative. That is, u × v ≠ v × u. The vectors u × v and v × u have the same magnitude but point in opposite directions.

Diagram showing vectors u and v with angle θ between them, and their cross product u×v pointing perpendicular (upward) to both.