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**1. Homework Statement**

Prove:

[tex]\int\left(\nabla \times \vec{F}\right)\cdot d\vec{V} = \oint \left(\vec{\hat{n}} \times \vec{F} \right) dS [/tex]

**2. Homework Equations**

In the previous part of the question, we proved that:

[tex]\nabla \cdot \left( \vec{F} \times \vec{d} \right) = \vec{d} \cdot \nabla \times \vec {F} [/tex]

(where

**d**is a constant vector)

And also, it looks like we'll need to use the Divergence theorem.

**3. The Attempt at a Solution**

OK, so, here I go!

[tex] \int\left(\nabla \times \vec{F} \right)\cdot \vec{\hat{n}}dV \\

= \int \nabla \cdot \left( \vec{F} \times \vec{\hat{n}} \right) dV [/tex]

By the relation above proved from the previous part of the question. Next, I used the divergence theorem:

[tex]

\int \nabla \cdot \left( \vec{F} \times \vec{\hat{n}} \right) dV = \oint \left( \vec{F} \times \vec{\hat{n}} \right) \cdot d\vec{S} [/tex]

My question is...Is [tex] \oint \left( \vec{F} \times \vec{\hat{n}} \right) \cdot d\vec{S} = \oint \left(\vec{\hat{n}} \times \vec{F} \right) \cdot d \vec{S} [/tex]?

My initial thought is that it isn't, as the cross product isn't commutative. If that is thecase, where else have I gone wrong?

Cheers!