(Solved): Use Stokes' theorem to compute the circulation \( \oint_{C} \vec{F} \cdot d \vec{r} \) where \( \ve ...

Use Stokes' theorem to compute the circulation \( \oint_{C} \vec{F} \cdot d \vec{r} \) where \( \vec{F}=\left\langle 7 x y z, 5 y^{2} z, 2 y z\right) \) and \( C \) is the boundary of the portion of the plane \( 2 x+3 y+z=6 \) in the first octant. Here \( C \) is positively oriented with respect to the plane whose orientation is upward.