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BUILT-IN MATHEMATICA SYMBOL
Cross 
Cross[a, b]
gives the vector cross product of a and b.
Details
- 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 EsccrossEsc b or 
. Note the difference between \[Cross] and \[Times]. - Cross is antisymmetric, so that Cross[b, a] is
. » - Cross[{x, y}] gives the perpendicular vector
. - In general, Cross[v1, v2, ..., vn-1] 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[v1, v2, ...] gives the dual (Hodge star) of the wedge product of the
, viewed as one-forms in n dimensions.
New in 3
