Answer
$(v, 3 \cos u, 3 \sin u)$ and $u \in (\dfrac{\pi}{2}, \dfrac{3 \pi}{2}); v \in (0,5)$
Work Step by Step
Since the given surface is part of the cylinder with the axis as the x-axis and with radius $3$, thus the equation of the full cylinder is: $y^2+z^2=3^2$
The parametric representation for the cylinder can be written as: $(v, 3 \cos u, 3 \sin u)$ and $ x$ varies from $0$ to $5$.
Therefore $v \in (0,5)$ and $y \in (0, -3); z \in (-3,3)$
This means that $-1 \lt \cos u \lt 0$ and $-1 \lt \sin u \lt 1$ and $u \in (\dfrac{\pi}{2}, \dfrac{3 \pi}{2})$
Thus, our answer is:
$(v, 3 \cos u, 3 \sin u)$ and $u \in (\dfrac{\pi}{2}, \dfrac{3 \pi}{2}); v \in (0,5)$
