Let C be the curve described by $\vec { r } ( t )$ .If the angle between $\vec { F } ( t )$ and $\vec { r } ^ { \prime } ( t )$ is less than $\pi$/2, then $\int _ { C } \vec { F } \cdot \overline { d r } \geq 0$

Question

Quizplus · Accepted Answer

If the angle between $\vec{F}(t)$ and $\vec{r}^{\prime}(t)$ is less than $\pi/2$, it means $\vec{F}$ and $\vec{r}^{\prime}$ have a positive dot product along the curve, making the integral $\int_{C} \vec{F} \cdot d\vec{r}$ non-negative.

Let C Be the Curve Described By r⃗(t)\vec { r } ( t )r(t)

Let C Be the Curve Described By $\vec { r } ( t )$