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Levi Civita proof  Curl 
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#1
Mar412, 01:39 PM

P: 29

I need to prove that [tex]\nabla \times (\vec{A} \times \vec{B}) [/tex]
Well. Trying to solve it, I've come to this: [tex]\partial_j \vec{A}_i \vec{B}_j \hat{u}_i \partial_i \vec{A}_i \vec{B}_j \hat{u}_j [/tex] Then I've found in my book that this is equal to: [tex]\vec{A}_i \partial_j \vec{B}_j \hat{u}_i + \partial_j \vec{B}_j \vec{A}_i \hat{u}_i  (\vec{A}_i \partial_i \vec{B}_j \hat{u}_j + \vec{B}_j \vec{A}_i \partial_i \hat{u}_j) [/tex] Can someone explain to me why? 


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