In high school we learn the line equation y = mx + c where m is the gradient and c is the intercept. However this form is problematic for vertical lines where m is infinite. A more powerful representation is the homogeneous form ax + by + c = 0 which can be represented by a 3-vector L = [a b c].

Given a pair of Cartesian points represented by 2-element column vectors P1 and P2 determine the equation of a homogeneous line of the form expressed as a 3-element row vector.