- #1

galactic

- 30

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**"Del" operator crossed with a scalar times a vector proof**

## Homework Statement

Prove the following identity (we use the summation convention notation)

[tex]\bigtriangledown\times(\phi\vec{V})=(\phi \bigtriangledown)\times\vec{V}-\vec{V}\times(\bigtriangledown)\phi[/tex]

## Homework Equations

equation for del, the gradient, curl..

## The Attempt at a Solution

im kind of confused on the first step...I broke it down into the following; however, levi civita symbols aren't my cup of tea and I get pretty confused about it...anyway here's what I did:

[tex]\bigtriangledown\times(\phi\vec{V})=(\epsilon_{ijk})\partial_i\vec{V}\phi\hat{x}_k[/tex]

I don't know if this first step is right or if I decomposed the cross product right ?

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