The Cartesian equation of a line through ($x_{1}$,$y_{1}$,$z_{1}$) with DRs (a,b,c) is $\frac{x-x_{1}}{a}$ = $\frac{y-y_{1}}{b}$ = $\frac{z-z_{1}}{c}$ = 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: $\frac{x-x_{1}}{a}$ = $\frac{y-y_{1}}{b}$, z = $z_{1}$. This means the line lies in the plane z = $z_{1}$. A common JEE mistake is forgetting to handle zero denominators.