Let $\vec { n }$ be the unit normal vector of S.If the angle between $\vec{F}$ and $\vec { n }$ is less than $\pi$/2 at each point of the surface, then $\int _ { S } \vec { F } \cdot \overrightarrow { d A } \geq 0$

Question

Let $\vec { n }$ be the unit normal vector of S.If the angle between $\vec{F}$ and $\vec { n }$ is less than  $\pi$/2 at each point of the surface, then $\int _ { S } \vec { F } \cdot \overrightarrow { d A } \geq 0$

Quizplus · Accepted Answer

If the angle between $\vec{F}$ and $\vec{n}$ is less than $\pi/2$, the dot product $\vec{F} \cdot \vec{n}$ is positive, but the integral $\int _ { S } \vec { F } \cdot \overrightarrow { d A }$ depends on the orientation of the surface and the vector field, so it is not guaranteed to be non-negative.

Let n⃗\vec { n }n Be the Unit Normal Vector of S

Let $\vec { n }$ Be the Unit Normal Vector of S