Vector Triple Product

Author

Eric W. Weisstein
April 14, 2004

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

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

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

Examples

𝒜=Array[a,3];
ℬ=Array[b,3];
𝒞=Array[c,3];

Subtract@@{Cross[𝒜,Cross[ℬ,𝒞]],ℬ 𝒜.𝒞-𝒞 𝒜.ℬ}//Simplify

Subtract@@{Cross[Cross[𝒜,ℬ],𝒞],-Cross[𝒞,Cross[𝒜,ℬ]]}//Simplify

Subtract@@{Cross[Cross[𝒜,ℬ],𝒞],-𝒜 ℬ.𝒞+ℬ 𝒜.𝒞}//Simplify