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 Fwhether 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: