(Solved): 9. Let \( \vec{F}=\left\langle 2 x y, x^{2}+e^{3 z}, 3 y e^{3 z}\right\rangle \). A. Calculate \( ...

9. Let \( \vec{F}=\left\langle 2 x y, x^{2}+e^{3 z}, 3 y e^{3 z}\right\rangle \). A. Calculate \( \operatorname{Curl}(\vec{F}) \) B. If \( \vec{F}=\left\langle 2 x y, x^{2}+e^{3 z}, 3 y e^{3 z}\right\rangle \) is a conservative vector field, then, find its potential function. C. Use calculus to calculate \( \int_{C} \vec{F} \cdot d \vec{r} \) for \( \vec{F}=\left\langle 2 x y, x^{2}+e^{3 z}, 3 y e^{3 z}\right\rangle \) on \( \mathrm{C} \) : the line segment from the origin to point \( (1,1,0) \), then, along a circular arc from point \( (1,1,0) \) to the point \( (2,3,1) \).