This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 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 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 ]. 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]=