Point and line duality
A line l is a homogeneous 3-vector
It is to every point (ray) p on the line:  l p=0
p2
l1
p
p1
l
l2
What is the line l spanned by rays p1 and p2 ?
l is to p1 and p2      l = p1 p2
l is the plane normal
What is the intersection of two lines l1 and l2 ?
p is to l1 and l2      p = l1 l2
Points and lines are dual in projective space
every property of points also applies to lines