Suppose a Curve C Is Parameterized By $\vec { r } ( t )$

Essay

Suppose a curve C is parameterized by $\vec { r } ( t )$ with $a \leq t \leq b$ and suppose $\vec { F }$ is a vector field $\vec{F}(t)=\vec{r}(t) \times \vec{r}^{\prime}(t)$ for $a \leq t \leq b$ .Explain why $\int _ { C } \vec { F } \cdot d \vec { r } = 0$