$P_{1},P_{2}$ are parts of $RP^{n}$ so that dim($P_{1}+P_{2}$)>1. I'm trying to prove that $P_{1}+P_{2}$ equals a union of all the lines in $RP^{n}$ that divide $P_{1}$ and $P_{2}$ in different points.
I started with what i know and that is that dim($P_{1}+P_{2}$)=dim$P_{1}$+dim$P_{2}$ - dim($P_{1}\cap P_{2}$)>1 Let's say $P_{1}$=P(V) and $P_{2}$=P(W) with V and W lineaire vector spaces of $R^{n-1}$. Now it follows that dimP(V)+dimP(W)+dim(P(V)$\cap$P(W)>0
and.. I'm already stuck.
My second guess was to dualise my question but i don't get any further.