Cross

Cross[a, b] gives the vector cross product of a and b.

If a and b are lists of length 3, corresponding to vectors in three dimensions, then Cross[a, b] is also a list of length 3.

Cross[a, b] can be entered in StandardForm and InputForm as a b, a cross b or a \[Cross] b. Note the difference between \[Cross] and \[Times].

Cross is antisymmetric, so that Cross[b, a] is -Cross[a, b].

In general, Cross[, , ... , ] is a totally antisymmetric product which takes vectors of length n and yields a vector of length n that is orthogonal to all of the .

Cross[, , ... ] gives the dual (Hodge star) of the wedge product of the , viewed as one-forms in dimensions.

See The Mathematica Book: Section 1.8.3.

See also: Dot, Signature, Outer.

Further Examples