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 , 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.
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