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Cross

Usage

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


Notes

• 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 AliasIndicatorcrossAliasIndicator b or a \[Cross] b. Note the difference between \[Cross] and \[Times].
Cross is antisymmetric, so that Cross[b, a] is -Cross[a, b].
Cross[{x, y}] gives the perpendicular vector {-y, x}.
• 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 Section 1.8.3.
• See also: Dot, Signature, Outer.
• New in Version 3.


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