The Cartesian equation of a line through (x_{1},y_{1},z_{1}) with DRs (a,b,c) is (x-x_{1})/a = (y-y_{1})/b = (z-z_{1})/c = lambda (say). Each value of lambda gives coordinates: x = x_{1}+a·lambda, y = y_{1}+b·lambda, z = z_{1}+c·lambda. If one DR is 0 (e.g., c = 0), write z = z_{1} separately: (x-x_{1})/a = (y-y_{1})/b, z = z_{1}. This means the line lies in the plane z = z_{1}. A common JEE mistake is forgetting to handle zero denominators.