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Let $\mathbf{F}$ be the vector field shown in the figure.

(a) If $C_{1}$ is the vertical line segment from $(-3,-3)$ to

$(-3,3),$ determine whether $\int_{C_{1}} \mathbf{F} \cdot d \mathbf{r}$ is positive, nega-

tive, or zero. (b) If $C_{2}$ is the counterclockwise-oriented circle with radius 3 and center the origin, determine whether $\int_{C_{2}} \mathbf{F} \cdot d \mathbf{r}$ is positive, negative, or zero.

a. Positive

b. Negative

Vector Calculus

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Johns Hopkins University

Harvey Mudd College

Idaho State University

Boston College

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