Is torsion $0$ for an osculating curve in Euclidean space

Question

A curve is called osculating curve if its position vector lies on its osculating plane. Osculating plane for the curve $\alpha(s)$ at some point on it is generated by the tangent vector and normal vector of $\alpha$ at that point. i.e.,
$\alpha(s)=\lambda_1(s)t(s)+\lambda_2(s)n(s)$, for some function for some function $\lambda_1(s)$ and $\lambda_2(s)$.
Is torsion $0$ for an osculating curve in Euclidean space?

Answer 1

HINT: Differentiate, use the Frenet equations, and then use linear independence of $T,N,B$.