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Cross

Cross
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 is also a list of length 3.
  • Cross gives the perpendicular vector .
  • 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 n dimensions.
The cross product of two vectors:
The cross product of a single vector:
Enter using Esc cross Esc:
The cross product of two vectors:
In[1]:=
Click for copyable input
Out[1]=
 
The cross product of a single vector:
In[1]:=
Click for copyable input
Out[1]=
 
Enter using Esc cross Esc:
In[1]:=
Click for copyable input
Out[1]=
Cross product computed with exact arithmetic:
Computed with machine arithmetic:
Computed with arbitrary-precision arithmetic:
Cross of one vector in 2 dimensions:
Cross product of three vectors in 4 dimensions:
Find the normal to the plane spanned by two vectors:
The equation for the plane:
Find a vector perpendicular to a vector in the plane:
Find a vector orthogonal to n - 1 vectors in n dimensions:
If u and v are linearly independent, u×v is nonzero and orthogonal to u and v:
If u and v are linearly dependent, u×v is zero:
Cross is antisymmetric:
For vectors in 3 dimensions, Cross is bilinear:
The (antisymmetric) matrices for the linear operators and :
New in 3