 |
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 and InputForm 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: Section 1.8.3.
See also: Dot, Signature, Outer.
Further Examples
This defines w to be the cross product of u and v.
In[1]:= 
In[2]:= 
In[3]:= 
Out[3]= 
The cross product of two vectors in three dimensions is perpendicular to the two vectors.
In[4]:= 
Out[4]= 
This is the generalized cross product of five vectors in six dimensions.
In[5]:= 
Out[5]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
| |
|
