# Prove that the following function is an orientation of a curve

Assume that $$f^{(j)}:\mathbb{R}^3\rightarrow \mathbb{R}$$ for $$j=1,2$$ are some $$C^1$$ functions such that $$(\nabla f^{(1)}, \nabla f^{(2)})$$ are independent over the curve $$\gamma = \{ x \in \mathbb{R}^3 | f^{(1)}(x)=0=f^{(2)}(x)\}$$. Prove that the function $$O :=sgn(det(\nabla f^{(1)} \nabla f^{(2)} u))$$ defines orientation for the curve $$\gamma$$.

I don't know how to approach this kind of question... What is the usual way to prove that some function defines orientation?