# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Cross

Cross[a,b]
gives the vector cross product of a and b.

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

The cross product of two vectors:

 In[1]:=
 Out[1]=

The cross product of a single vector:

 In[1]:=
 Out[1]=

Enter using EsccrossEsc:

 In[1]:=
 Out[1]=