# Question on Stokes theorem

I have a question relating an identity using Stokes theorem.

$$\iint_A \left( \nabla \otimes \vec{F}\right) \cdot \vec{dA} = \oint_c \vec{F} \cdot \vec{dr}$$

But my professor mentioned something about the divergence theorem

$$\int_V \left( \nabla \cdot \vec{F} \right)dV = \oint_{\partial V} \vec{F} \cdot \vec{dA}$$

so does this mean I can say:

$$\iint_A \left( \nabla \otimes \vec{F}\right) \cdot \vec{dA} = \oint_c \vec{F} \cdot \vec{dr} = \iint_A \left( \nabla \cdot \vec{F} \right) dA$$

Because this would imply:

$$\left( \nabla \otimes \vec{F}\right) \cdot \vec{dA}= \left( \nabla \cdot \vec{F} \right) dA$$

And I don't believe this to be correct. Thank you for your help in advance!

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