I have an exercise in geometry that works with plane curves. For starters, it fixes an orientation on the vector plane $\stackrel{\to}{P}$ and states that $J: \stackrel{\to}{P} \to \stackrel{\to}{P}$ is the 90 degrees rotation in the sense of orientation.

I wonder **what to "fix an orientation means"**, is it to fix a basis and give an order between the basis?. 

The exercise then ask me to prove that tangent $t(s) = \alpha'(s)$ and normal $J(t(s))$ form a positive orthonormal basis of $\stackrel{\to}{P}$. 

To see that the basis is orthonormal is easy. But how can I **show the basis is oriented positively with respect to the original one**?