I'm having trouble trying to start this. Here is the problem statement:
Show that if $w : S \to \mathbb{R^3}$ is a differentiable vector field on a regular surface $S \subset \mathbb{R}^3$, and $w(p) \neq 0$ for some $p \in S$, then it is possible to parametrize a neihghborhood of $p$ by $x(u,v)$ in such a way that $x_u = w$.
How do I start this? What do I need to show to prove this?