The figure shows a vector field $\vec{F}$ and three paths from $P = (-3,0)$ to $Q = (3,0)$. The top and bottom paths $T$ and $B$ comprise a circle, and the middle path $M$ is a line segment. Determine whether the following quantities are positive, negative, or zero, or answer true or false. Be sure you can explain your answers. (a) $\displaystyle \int_T \vec{F} \cdot d\vec{r}$ is ? Positive Negative Zero (b) $\displaystyle \int_M \vec{F} \cdot d\vec{r}$ is ? Positive Negative Zero (c) $\displaystyle \int_B \vec{F} \cdot d\vec{r}$ is ? Positive Negative Zero (d) $\displaystyle \int_{T-B} \vec{F} \cdot d\vec{r}$ is ? Positive Negative Zero (e) ? True False True or False: $\displaystyle \int_{-B} \vec{F} \cdot d\vec{r} = \int_{T} \vec{F} \cdot d\vec{r}$ (f) ? True False True or False: $\vec{F}$ is a gradient field.

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You can earn 50% partial credit for 3 - 5 correct answers.