Answer
$( r \cos \theta, r \sin \theta, r \cos \theta+3)$ and $\theta \in (0, 2 \pi); |r| \lt 1$
Work Step by Step
The points on the plane are $z=x+3$ and the points inside the cylinder are of the form $x= r \cos \theta; y= r \sin \theta$ and $z=z$
Where $\theta \in (0, 2 \pi); |r| \lt 1$
The part on the plane inside the cylinder can be written as: $z=r \cos \theta +3$
So, the points on the plane which are inside the cylinder can be described as:
$ (x,y,z)=( r \cos \theta, r \sin \theta, r \cos \theta+3)$ and $\theta \in (0, 2 \pi); |r| \lt 1$
Our answer is: $( r \cos \theta, r \sin \theta, r \cos \theta+3)$ and $\theta \in (0, 2 \pi); |r| \lt 1$
