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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 ab, 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

    This defines w to be the cross product of u and v.

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    The cross product of two vectors in three dimensions is perpendicular to the two vectors.

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    This is the generalized cross product of five vectors in six dimensions.

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