Answer
Result $c = \frac{3}{2\pi}$,
Work Step by Step
For one complete turn of the helix, $\theta = 2\pi$:
$\mathbf{r}(0) = a\cos 0 \mathbf{i} + a\sin 0 \mathbf{j} + 0 = a\mathbf{i}$
and
$\mathbf{r}(2\pi) = a\cos 2\pi \mathbf{i} + a\sin 2\pi \mathbf{j} + c(2\pi)\mathbf{k} = a\mathbf{i} + c(2\pi) \mathbf{k}$
It is given that
$2\pi c = 3 \implies c = \frac{3}{2\pi}$.
Result: $c = \frac{3}{2\pi}$
