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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

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