Let C be the counter-clockwise planar circle with center at the origin and radius r $>$ 0. Without computing them, determine for the following vector fields $\bf F$ whether the line integrals $\displaystyle \int_C \mathbf F \cdot \, d\mathbf{r}$ are positive, negative, or zero and type P, N, or Z as appropriate.

A. $\bf F$ = the radial vector field = $x\mathbf i + y\mathbf j$:

B. $\bf F$ = the circulating vector field = $-y\mathbf i + x\mathbf j$:

C. $\bf F$ = the circulating vector field = $y\mathbf i - x\mathbf j$:

D. $\bf F$ = the constant vector field = $\bf i + j$: