Parametrized curve $\alpha$ with $||\alpha'(t)||= k \neq 0$ For a parametrized curve $\alpha:I \rightarrow \mathbb{R}^3$ and $k \in \mathbb{R} - \{0\}$, we have:
$$\|\alpha'(t)\|= k \iff \alpha'(t) \perp \alpha''(t)$$
$$\forall t \in I.$$
I did the "$\Rightarrow$" proof, but I couldn't think about the "$\Leftarrow$".
Any hints?

Hint :$<a',a'>'=2<a',a''>=0$...can you take it from here?
