Cross Product

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/CrossProduct.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CrossProduct.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Definition

{{xhat,yhat,zhat},u/@{x,y,z},v/@{x,y,z}}//MatrixForm

Collect[Det[{{xhat,yhat,zhat},u/@{x,y,z},v/@{x,y,z}}],{xhat,yhat,zhat}]

Tensor Form

Collect[Sum[x[i]A[j]B[k]Signature[{i,j,k}],{i,3},{j,3},{k,3}],{x[1],x[2],x[3]}]

Collect[Det[{{x[1],x[2],x[3]},A/@{1,2,3},B/@{1,2,3}}],{x[1],x[2],x[3]}]