TITLE: What is the interpretation of homogeneous line intersection?
QUESTION [7 upvotes]: I understand homogeneous coordinate systems. I read the intersection of lines in homogeneous coordinate can be computed by taking a cross products of lines $l_1(a_1,b_1,c_1)$ and $l_2(a_2,b_2,c_2)$.
I can see how this computationally matches. My question is, is there any intuitive/figurative meaning to it? Why does cross product serve this purpose?

REPLY [2 votes]: @MvG has answered it and I accepted it. I just wanted to post a picture I've drawn for this to help me understand in case if someone else finds it useful.