Derivative with the double cross product

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Vectronix
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Is there a spatial derivative that uses the del operator and the double cross product? If so, is it used in physics?
 
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I am not sure what you mean by double cross product. Here is a quick reference for uses of the ∇ operator. https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/4.-triple-integrals-and-surface-integrals-in-3-space/part-c-line-integrals-and-stokes-theorem/session-90-curl-in-3d/MIT18_02SC_MNotes_v15.1.pdf