Does this question about planes p1 & p2 & line L1 make sense, or is it flawed

Given line L1 is parallel to, but not contained in plane p1. Plane p2 contains the same line L1 and is perpendicular to plane p1. Is the about statement flawed?? How can a line be parallel to, but not on the first plane yet contained on a second plane that is perpendicular to the first plane? Please help. Thanks very much. I think the statement is flawed.

Consider the xy- plane and the line parallel to the y-axes at z=1 and in the yz- plane....the yz- plane is perp to the xy- plane, so this is an example of the situation described. Not flawed therefore...

Nothing wrong with the statement.
Consider the screen to be one plane
hold a pencil up in front of it
as long as the pencil is parallel to some line in the screen it is parallel to the screen
that means the you can rotate the pencil through 360° and any of those positions are parallel to the screen (In other words another plane parallel to the first can contain lines having any direction in that plane, 360°)
Drawing a line in the first plane directly "under" the pencil (closest to each point in the line that the pencil represents) will give you two parallel lines. Only one plane can contain both of those lines, a plane perpendicular to the first (and second) plane.
easy.
The cross section of the three planes would look like this ╫

The statement is flawed. the line passes through p2 but cannot be contained in p2 for if it was it would not be parallel to p1