Given three lines, $L, M, N \in\mathbb{P}^4$, not in one hyperplane and not pairwise intersecting, I need to calculate
$$\dim(\langle L,M\rangle\cap N)$$.
I can however not find a definition for pairwise non-intersecting lines. How do I think about pairwise non-intersecting lines in $\mathbb{P}^4$?
It's simple. $L,M,N$ are pairwise non-intersecting if each pair doesn't intersect; that is, $L\cap M$, $M\cap N$, and $N\cap L$ are all empty.
This principle applies to many other "pairwise X" phrases as well.