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 given by $z=x+3$ and the points inside the cylinder are of the form $x= r \cos \theta; y= r \sin \theta; z=z$
and $\theta \in (0, 2 \pi); |r| \lt 1$
Since, the part on the plane inside the cylinder is: $z=r \cos \theta +3$, therefore, he 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 result is: $( r \cos \theta, r \sin \theta, r \cos \theta+3)$ and $\theta \in (0, 2 \pi); |r| \lt 1$
