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

Using index notation to prove

[tex]\vec{\nabla}\times\left(\vec{A}\times\vec{B}\right) = \left(\vec{B}\bullet\vec{\nabla}\right)\vec{A} - \left(\vec{A}\bullet\vec{\nabla}\right)\vec{B} + \vec{A}\left(\vec{\nabla}\bullet\vec{B}\right) - \vec{B}\left(\vec{\nabla}\bullet\vec{A}\right)[/tex]

2. Relevant equations

--?

3. The attempt at a solution

I tried converting the right side first...

[tex]B_{a}A_{k,a}-A_{a}B{k,a}+A_{a}\epsilon_{abc}B_{b,c}-[/tex][tex]B_{a}\epsilon_{abc} A_{b,c}[/tex]

but i don't really know if this is right... i'm very very new to the index notation system. i don't really understand the rules beyond the basics. will someone please give me some clue as to where to go from here?

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# Homework Help: Vector identity proof using index notation

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