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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 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].
• 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  .
• See also:


Using InstantCalculators

Here are the InstantCalculators for the Cross function. Enter the parameters for your calculation and click Calculate to see the result.

Entering Commands Directly

You can paste a template for this command via the Text Input button on the Cross Function Controller.

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

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

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

Ordinary Mathematical Notation

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

Clear the variable definitions.

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