(a) Find a vector-parametric equation $\vec{r}_1(t) = \langle x(t), y(t), z(t) \rangle$ for the shadow of the circular cylinder $x^2 + z^2 = 9$ in the $xz$-plane.

Shadow: $\vec{r}_1(t) =$ for $0 \leq t \leq 2\pi$.

(b) Find a vector-parametric equation for intersection of the circular cylinder $x^2 + z^2 = 9$ and the plane $3 x + 6 y + 8 z = 1$.

Intersection: $\vec{r}_2(t) =$ for $0 \leq t \leq 2\pi$.