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# Curl and cros product question watch

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1. 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...?
2. (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:

Expanding out the second cross product and with a few rearrangements, you should be able to obtain the right hand side.
3. (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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