In our book of analytic geometry we have a title The canonical form of a line. It is the equation of a line passing through a point $p_1 := (x_1 , y_1,z_1)$ and parallel to a vector whose direction ratio is $a:b:c$.
Under another title The Symmetric (Two point) form of a line is the equation of a line passing through the 2 points $p_1 = (x_1, y_1, z_1)$ and $p_2 = (x_2 , y_2 , z_2)$. so what is the difference between both of them?? I can figure out the difference between them and the parametric form but those two can't get it???!! am so confused