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## Homework Statement

Prove that

## \oint_{\partial S} ||\vec{F}||^2 d\vec{F} = -\int\int_S 2 \vec{F}\times d\vec{A} ##

## Homework Equations

Identities:

##\nabla \times (||\vec{F}||^2 \vec{k}) = 2\vec{F} \times \vec{k} ##

For ##\vec{k} ## constant i.e. ## \nabla \times \vec{k} = 0 ##

Stokes Theorem

##\oint_{\partial S} \vec{B} \cdot d\vec{x} = \int\int_S (\nabla \times \vec{B})\cdot d \vec{A} ##

## The Attempt at a Solution

So I need to use that identity ##\nabla \times (||\vec{F}||^2 \vec{k}) = 2\vec{F} \times \vec{k} ##

The problem is that Stokes theorem is in a different form. The constant vector here I think is the

**k**=d

**A**.

I really can't think of what to do

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