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    I need to prove this
    ∇×(a×b)=a(∇⋅b)+(b⋅∇) a−b(∇⋅a)−(a⋅∇)b

    I can work out a x b (I think!) but then I don't know how to take the curl of that and where does the dot product in the answer come from...?
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    (Original post by Beth_Sugar)
    I need to prove this
    ∇×(a×b)=a(∇⋅b)+(b⋅∇) a−b(∇⋅a)−(a⋅∇)b

    I can work out a x b (I think!) but then I don't know how to take the curl of that and where does the dot product in the answer come from...?
    Hi there, a better place for this thread might be here:
    As for your question:
    Are you familiar with suffix notation? The left hand side is:
    \epsilon_{ijk}\nabla_j(\mathbf{a  } \times \mathbf{b})_k
    Expanding out the second cross product and with a few rearrangements, you should be able to obtain the right hand side.
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    (Original post by Beth_Sugar)
    I need to prove this
    ∇×(a×b)=a(∇⋅b)+(b⋅∇) a−b(∇⋅a)−(a⋅∇)b

    I can work out a x b (I think!) but then I don't know how to take the curl of that and where does the dot product in the answer come from...?
    http://www.thestudentroom.co.uk/show....php?t=3349619
 
 
 
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