Condition for feet of common perpendicular on two skew lines for JEE

Formula

\((\vec r_2-\vec r_1)\cdot\vec b_1=0,\quad (\vec r_2-\vec r_1)\cdot\vec b_2=0\)

Variables: \(\vec r_1=\vec a_1+\lambda\vec b_1\) and \(\vec r_2=\vec a_2+\mu\vec b_2\) are variable points on the two skew lines.

Conditions: Used to determine parameters \(\lambda,\mu\) of the feet of the common perpendicular.

Finding actual endpoints of shortest distance segment and then its equation.