# Index notation for vector id's

#### flame_m13

1. The problem statement, all variables and given/known data
Prove vector identity $$\nabla$$ x$$\nabla\phi$$ = 0 using index notation.

2. Relevant equations

$$\nabla$$ x A = Ejrt$$\partial$$rAt

3. The attempt at a solution
I'm treating this as $$\nabla$$x A, where A = del $$\Phi$$ = Etpq$$\partial$$p$$\Phi$$q

putting A back in the equation:

= EjrtEtpq$$\partial$$r$$\partial$$p$$\Phi$$q

=EtrjEtpq$$\partial$$r$$\partial$$p$$\Phi$$q

=($$\partial$$jp$$\partial$$rq - $$\partial$$jq$$\partial$$rp)$$\partial$$r$$\partial$$p$$\Phi$$q

It's here that I'm stuck. I know it should be simple after this, and somehow I need to get zero, but I'm completely stuck. Maybe I messed up somewhere?

#### tiny-tim

Science Advisor
Homework Helper
Hi flame_m13!

(have a del: ∇ and a curly d: ∂ )
… where A = del $$\Phi$$ = Etpq$$\partial$$p$$\Phi$$q
Nooo … (∇φ)p = ∂pφ

#### flame_m13

thanks. i have skill at making things unnecessarily complicated. :)

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