Parametric equation of a line through a point for JEE

Formula

\(x=x_1+a\lambda,\quad y=y_1+b\lambda,\quad z=z_1+c\lambda\)

Variables: \((x_1,y_1,z_1)\) is a point on the line; \((a,b,c)\) are direction ratios; \(\lambda\in\mathbb{R}\) is parameter.

Intersection, shortest distance, image of moving point, elimination of parameter.