Example

If $\underline{F}=\underline{r}$, then $\nabla \times \underline{r}=0$ (example A.2.4), and the LHS of (A.16) is zero. Therefore the RHS must also be zero: if $\underline{r}$ is the vector distance from a fixed origin to a point of an arbitrary closed contour $l$, the the integral of $\underline{r} \cdot \hat{l}$ along the contour is always zero.