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Curl and cros product question

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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Avatar for joostan
joostan
13
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:
ϵijk∇j(a×b)k\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.
Reply 2
Avatar for TeeEm
TeeEm
19
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/showthread.php?t=3349619

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