Intersecting lines condition via parameters for JEE

Formula

\(x_1+a_1\lambda=x_2+a_2\mu,\quad y_1+b_1\lambda=y_2+b_2\mu,\quad z_1+c_1\lambda=z_2+c_2\mu\)

Variables: Two lines are \(x=x_1+a_1\lambda, y=y_1+b_1\lambda, z=z_1+c_1\lambda\) and \(x=x_2+a_2\mu, y=y_2+b_2\mu, z=z_2+c_2\mu\).

Conditions: A common solution \((\lambda,\mu)\) implies intersection.

Testing whether two lines intersect and finding point of intersection.