Problem on qualitative evaluation of a line integral

Without calculation, determine if $\int_C \mathbf{F}\cdot d\mathbf{r}$ is positive, negative, or zero. $\mathbf{F}$ is the vector field pictured below. $C$ is the line segment traced out as indicated.
• Solution

Recall that
As suggested, we determine the sign of $\mathbf{F} \cdot d\mathbf{r}$ along $C$.
It appears that $\mathbf{F}$ points in the direction of $\mathbf{i} + \mathbf{j}$ or $-\mathbf{i} - \mathbf{j}$.
Recall that $d\bfr$ is a small tangent vector along the curve $C$. It looks like $d\mathbf{r}$ points in the direction of $\mathbf{i} - \mathbf{j}$.
Thus, it appears that $\bfF$ is perpendicular to $d\bfr$.
Recall that
Hence $\bfF\cdot d\bfr = 0$.
Because the integrand is always 0, $\int_C \mathbf{F}\cdot d\mathbf{r}$ is zero.