I am pretty new to projective space, and I sometimes struggle with simple problems like this one.
In a projective space $\mathbb{P}_n$, let $\pi_1, \pi_2$ be two disjoint planes. If lines $l,r$ intersect the planes in different points, prove $l$ and $r$ are disjoint.
I have tried to use Grassmann formula but I can't find the right way.
Any help or hint would be appreciated.