I have this problem where I have two lines given and I have to find a transversal. However, it also has to be perpendicular to a given plane (lines are not necessarily in the given plane).
My guess was that I would have to find perpendicular lines to the plane and then see if they are also transversals of those lines. But I've been stuck. Is this the right approach? Or should I start working from the lines and then tend to the plane and transversal being perpendicular?
If $r$ and $s$ are the lines and $\vec v$ is a vector perpendicular to the plane (which shuold be easy to obtain), the plane generated by the line $r$ and the vector $\vec v$ should intersect $s$ at one point $P$. The line that passes through $P$ and is parallel to $\vec v$ should meet the conditions.