Equation of the common perpendicular through one foot point for JEE

Formula

\(\vec r=\vec r_1+t(\vec b_1\times\vec b_2)\)

Variables: \(\vec r_1\) is one foot of the common perpendicular on the first line; \(t\in\mathbb{R}\).

Conditions: \(\vec r_1\) must satisfy the foot conditions with some point on the second line.

Writing the equation of the shortest-distance line once a foot point is known.