Wolfram Language & System 11.0 (2016)|Legacy Documentation

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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 EsccrossEsc 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[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 vi.
  • Cross[v1,v2,] gives the dual (Hodge star) of the wedge product of the vi, viewed as oneforms in n dimensions.
Introduced in 1996