We have to evaluate integral
$$ \int_c \vec{f(r}) . d\vec{r}$$
where c is the circle of radius b originated in the countercheck wise direction.
Let's define two functions.
$$1. \ \ \vec{f(r)} = x \hat{i} + y \hat{j}$$ $$2. \ \ \vec{f(r)} = - y \hat{i} + x \hat{j}$$
I have the solution of this two questions. The author says that the direction of the position vector of the first one is always perpendicular to the tangential direction and therefore we don't need to parametrize to find out the integral. And it is zero. On the other hand, the angle is $0^0.$ I don't understand how the angle works in this case. Could you please explain the cenerio?