# Normal vector to a surface and binormal vector to a curve that lies on the surface

Is the normal vector to a surface on the same direction as the binormal vector to a curve that lies on the surface ? To be more precise, consider a curve $\alpha(s)$ such that $a'(0) = v \in T_{p}S$ and $\alpha(0)= p$. My question is: does the normal vector to a surface at the point P correspond to the binormal vector (as in the Frenet frame) of $\alpha$ at 0?

I'm almost sure that this is true, however, I'd like to read others' opinion. Thank you.