- #1
darthvishous
- 2
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Homework Statement
I am trying to prove
$$\vec{\nabla}(\vec{a}.\vec{b}) = (\vec{a}.\vec{\nabla})\vec{b} + (\vec{b}.\vec{\nabla})\vec{a} + \vec{b}\times\vec{\nabla}\times\vec{a} + \vec{a}\times\vec{\nabla}\times\vec{b}.$$ I can go from RHS to LHS by writng $$\vec{b}\times\vec{\nabla}\times\vec{a}$$ as $$\epsilon_{ijk}b_k\epsilon_{klm}\partial_la_m=b_j\partial_ia_j-a_j\partial_jv_i$$, but I am unable do it the other way. Any help is appreciated.