Let $\vec F = (3x,4y,2z)$. Let $S$ be the surface parametrized by $\vec r(u,v) = (u,v,9-u^2-v^2)$.
- Compute $d\sigma$.
- State a unit normal vector $\hat n$ to the surface that points upwards at all points along the surface.
- Compute $\vec F\cdot\hat n d\sigma$. What does this quantity represent?
- Change the surface to the 6 faces of a rectangular box with $x\in [0,2], y\in [0,3], z\in [0.5] $. For each surface, state a normal vector and $\vec F\cdot\hat n d\sigma$.
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |