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) Where A and B are 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?