This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Documentation / Mathematica / Built-in Functions / New in Version 3.x / Lists and Matrices /

Cross

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

FilledSmallSquare 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.

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

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

FilledSmallSquare 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 .

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

FilledSmallSquare See Section 1.8.3.

FilledSmallSquare See also: Dot, Signature, Outer.

FilledSmallSquare New in Version 3.

Further Examples