Consider the vector field $\vec{F}$ in the figure and the closed circular path $C$ oriented counter-clockwise. (a) Is $\displaystyle \int_C \vec{F} \cdot d\vec{r}$ positive, negative, or zero? ? Positive Negative Zero (b) True or False: $\vec{F} = \mathrm{grad} f$ for some function $f$. Hint: use your answer to part (a). ? True False (c) Which of the following formulas best fits $\vec{F}$? A. $\displaystyle \vec{F} = y\vec{i} - x\vec{j}$ B. $\displaystyle \vec{F} = \frac{x}{(x^2+y^2)^2}\vec{i} + \frac{y}{(x^2+y^2)^2}\vec{j}$ C. $\displaystyle \vec{F} = \frac{y}{(x^2+y^2)^2}\vec{i} - \frac{x}{(x^2+y^2)^2}\vec{j}$ D. $\displaystyle \vec{F} = x\vec{i} + y\vec{j}$

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In order to get credit for this problem all answers must be correct.