(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the following vector identity:

[tex]\nabla[/tex]x(AxB) = (B.[tex]\nabla[/tex])A- (A.[tex]\nabla[/tex])B+A([tex]\nabla[/tex].B) -B([tex]\nabla[/tex].A)

WhereAandBare vector fields.

2. Relevant equations

Curl, divergence, gradient

3. The attempt at a solution

I think I know how to do this: I have to expand out the LHS and the RHS and show that they equal one another. To do this I need to use the product rule when taking the gradient of components with more than one term multiplied together.

What I don't understand is what's going on on the RHS: doesn't (B.[tex]\nabla[/tex])A=B([tex]\nabla[/tex].A) ? (Obviously this can't be the case since then all the components would cancel to zero.) So how does this really work?

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# Homework Help: Proving vector identities

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