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: