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 as a
b, 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 on the web:Section 1.8.3.
See also: Dot, Signature.
Further Examples
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