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The vector triple product of three vectors \vec{ \mathbf{v} }, \vec{ \mathbf{u} }, and \vec{ \mathbf{w} } is the cross product of one vector with the cross product of the other two. It is often used in vector calculus, as the vector Laplacian is a special case of the vector triple product.

Properties

  • \vec{ \mathbf{v} } \, \times \, \vec{ \mathbf{w} } \, \times \, \vec{ \mathbf{u} } = 
\vec{ \mathbf{w} } \, ( \vec{ \mathbf{v} } \, \cdot \, \vec{ \mathbf{u} } ) -

\vec{ \mathbf{u} } \, ( \vec{ \mathbf{v} } \, \cdot \, \vec{ \mathbf{w} } )

See also

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