True/False: If $\alpha(t)$ is a regular parametrized curve such that $\alpha'(t) \neq 0 $ for any t, then the derivative of the unit binormal with respect to arclength is always parallel to the unit normal.
I think this is false, since $T$ and $N$ are perpendicular, and $B = T \times N$ and $B' = \tau*N$, then $B'$ should not be parallel to $N$.
Could anyone better explain this to me?
Thank you in advance!