13. Which of the following is correct?
a. If $\vec{F}$ is conservative, then $\int_{C_1} \vec{F} \cdot d\vec{r} = \int_{C_2} \vec{F} \cdot d\vec{r}$ for any two smooth curves $C_1$ and $C_2$.
b. If $\vec{F}$ is conservative, then $\iint_S \vec{F} \cdot d\vec{S} = 0$.
c. If $\vec{F}$ is conservative, then div $\vec{F} = 0$.
d. If $D$ is a simply connected planar region, then the area of $D$ is $\oint_{\partial D} \frac{y}{2} dx - \frac{x}{2} dy$, where $\partial D$ is oriented counterclockwise.
e. If $\vec{F} = (x, -2y, z)$, then $\iint_S \vec{F} \cdot d\vec{S} = 0$, where $S$ is a unit sphere.