# Vector identities in index notation

1. Apr 25, 2009

### trv

1. The problem statement, all variables and given/known data

Prove using index notation that,

the x denoting a cross-product.

(del x f del g)=del f x del g

2. Relevant equations

3. The attempt at a solution

dif etc. denote partial derivatives.

RHS=eijkdjfdkg

LHS-I'm not even quite sure how to write it in index notation. Here's my attempt however.

LHS=eijk dj (fdkg)

But then if I write it like that, I can't tell the difference between LHS and RHS.

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Also can someone check whether the following are correct,

A.B=AiBi=AiBi

(A x B)i=eijkAjBk

Last edited: Apr 25, 2009
2. Apr 25, 2009

### dx

Hint: εijkjkg = -εikjkjg = -εijkjkg

Yes, that's correct.