Consider the space curve $\vec{r}(t) = (5t, 3\cos(t), 3\sin(t))$.
a. Find the arc length function for $\vec{r}(t)$.
$s(t) = \int_0^t ||\vec{r}'(\tau)|| d\tau =$
b. Find the arc length parameterization for $\vec{r}(t)$.
$\vec{r}(s) = (\frac{5s}{\sqrt{34}}, 3\cos(\frac{s}{\sqrt{34}}), 3\sin(\frac{s}{\sqrt{34}}))$.