How to use homogeneous coordinates and the projective plane to study the intersection of two lines, and how to compare this to a standard homogeneous coordinates. *The equation of a line in inhomogeneous coordinates is a · x + b · y + c = 0, for some a, b, c ∈ R
What do we get for the intersection in * homogeneous coordinates, * inhomogeneous coordinates if the lines are parallel, and non parallel. What do we get for the equation of the line passing through two points p1, p2 (in homogeneous coordinates)?
You can have the equation of a line through two points in the projective plane with determinant: $$\begin{vmatrix}x_1&x_2&X\\ y_1&y_2&Y\\t_1&t_2&T\end{vmatrix}=0.$$