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## Homework Statement

Show that for any scalar field α and vector field B:

∇ x (αB) = ∇α x B + α∇ x B

## Homework Equations

(∇ x B)

_{i}= ε

_{ijk}v

_{k,j}

(∇α)

_{i}= α

_{i}

(u x v)

_{i}= e

_{ijk}u

_{j}v

_{k}

## The Attempt at a Solution

Since α is a scalar i wasn't quite sure how to cross it with ∇

So on the left side I have:

ε

_{ijk}B

_{k,j}α

_{i}

I'm pretty sure I'm supposed to solve out the left side to get to the right because that what I did for the previous problem.

The right side all I could get it to simplify to was:

α

_{i}x B + α∇ x B