How can I find a fourth line $L$ that intersects three given lines $L_1$, $L_2$, $L_3$ in 3D space?
We can assume that $L_1$, $L_2$, $L_3$ are in "general position", so no two of them are coplanar, etc.
I'm not even sure that three lines is enough to uniquely define $L$, actually. If three lines is not enough, how many do I need?
The question is related to this one. Specifically, see idea #4 in my list of suggested approaches. It requires finding a line that intersects with a few given ones.
Apparently, I need four lines, not three, to uniquely define $L$. So, how can I construct a fifth line that interesects four given ones?