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Let $C$ be a circle of radius one lying on the plane $x+y+z = 6$. Calculate the circulation of:

$$\vec{F} = \langle e^{y+x} + 2xy, xy^2 + y^2z, 6y-x^2 \rangle$$

...about $C$ in the clockwise direction when viewed as in the figure.

$0$

$2\sqrt{3}$

$2\pi\sqrt{3}$

$6\pi$

None of the Above