1. Let $\alpha(t) = (r \cos t, r \sin t, ht)$, $t \in \mathbf{R}$, where $r > 0$, $h > 0$ are constant.
(i) Prove that $\alpha$ is a regular curve.
(ii) Find the velocity vector, the speed and the acceleration vector of $\alpha$.
(iii) Find the arc-length function, $h(t)$, for $\alpha$ and use it to find the unit speed reparametrisation of $\alpha$.
(iv) Find the curvature of $\alpha$.
(v) Find the torsion of $\alpha$.
