I'm having trouble with this question:
Choose a volume form $\zeta$ on the disk $D(r) = \{(x,y,0)\in \mathbb{R}^3:x^2+y^2\leq r^2\}$ and describe what the induced orientation 1-form looks like in the point $(r,0,0)$.
I tried to solve this, but end up with a volume form of $0$. This shouldn't happen. Any help is greatly appreciated.