I am trying to calculate the intersection point (if any) of two line segments for a 2D computer game. I am trying to use this method, but I want to make sure I understand what is going on as I do it. This method talks about using cross-products, and calculating that by using the determinant of the 2x2 matrix: (x1y2) - (x2y1).
My confusion comes from my remembering that a cross-product gives a vector perpendicular to the others... but it seems to me that calculating that determinant should just give a scalar - we end up with a single number at the end of it.
Where is my misunderstanding?