# Levi Civita proof - Curl

by cristina89
Tags: civita, curl, levi, proof
 P: 29 I need to prove that $$\nabla \times (\vec{A} \times \vec{B})$$ Well. Trying to solve it, I've come to this: $$\partial_j \vec{A}_i \vec{B}_j \hat{u}_i- \partial_i \vec{A}_i \vec{B}_j \hat{u}_j$$ Then I've found in my book that this is equal to: $$\vec{A}_i \partial_j \vec{B}_j \hat{u}_i + \partial_j \vec{B}_j \vec{A}_i \hat{u}_i - (\vec{A}_i \partial_i \vec{B}_j \hat{u}_j + \vec{B}_j \vec{A}_i \partial_i \hat{u}_j)$$ Can someone explain to me why?