# What are pairwise non-intersecting lines in $\mathbb{P}^4$

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.
• If we said they don't intersect, we would be saying that the triple intersection $L\cap M\cap N$ is empty - a much weaker condition. – jmerry Mar 27 at 22:09