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 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]. »
  • 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 one‐forms in n dimensions.

Examples

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Basic Examples  (3)

The cross product of two vectors:

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The cross product of a single vector:

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Enter using cross:

In[1]:=
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Out[1]=

Scope  (3)

Generalizations & Extensions  (3)

Applications  (3)

Properties & Relations  (5)

See Also

Dot  Signature  Outer  Curl  TensorWedge  LeviCivitaTensor  HodgeDual  KroneckerProduct  Orthogonalize  VectorAngle

Tutorials

Introduced in 1996
(3.0)