A Stokes' Theorem problem.

Question

I know this is Stokes' Theorem.

How should I proceed to proof that by dotting a constant vector on both sides I get the answer . $\phi$ is a scalar.

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Prove $$ \oint_C\phi\,\mathrm d\mathbf r = \iint_S\mathrm d\mathbf S\times\nabla \phi $$