Vector Equation | Proving ∇×(a × b)

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SUMMARY

The vector equation ∇×(a × b) is proven to be equal to a(∇ · b) − b(∇ · a) + (b · ∇)a − (a · ∇)b. The initial incorrect assumption was that ∇×(a × b) equals a(∇b) - b(∇a). The correct proof involves understanding the properties of vector calculus, specifically the curl and divergence operations applied to vector fields.

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vector equation [SOLVED]

Hello, I'm trying to proof that
∇×(a × b) = a(∇ · b) − b(∇ · a) + (b · ∇)a − (a · ∇)b
(where a & b are vectors)

But I'm stuck...

Probably because this isn't correct:

∇×(a × b) = a(∇b) - b(∇a) ?

But i don't know why!

Could somebody please help !
Kind regards
 
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