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

Prove the vector identity: [tex]\left(a\times\nabla\right)\bullet\left(u \times v\right)=\left(a \bullet u \right)\left(\nabla \bullet v \right)+\left(v \bullet \nabla \right)\left(a \bullet u \right)-\left(a \bullet v \right)\left(\nabla \bullet u \right)-\left(u \bullet\nabla\right)\left(a \bullet v \right)[/tex]

Where a, u, and v are vectors (and a is a "constant vector")

2. Relevant equations

N/A

3. The attempt at a solution

Okay, so in index notation I've gotten the left-hand side as...

[tex]LHS=a_{l}u^{l}\partial_{m}v^{m}-a_{m}v^{m}\partial_{l}u^{l}[/tex]

Which, since the dot product on the RHS is commutative, it seems that the RHS is just twice the LHS I've come up with in index notation. What am I missing here? Is there some weird property of the del operator in index notation that I can just double the terms?

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# Homework Help: Proving vector identities with index notation (help with the del operator)

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