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Levi Civita proof - Curl

by cristina89
Tags: civita, curl, levi, proof
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cristina89
#1
Mar4-12, 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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