Shortest distance between parallel lines for JEE

Formula

\(d=\frac{|(\vec a_2-\vec a_1)\times\vec b|}{|\vec b|}\)

Variables: Parallel lines are \(\vec r=\vec a_1+\lambda\vec b\) and \(\vec r=\vec a_2+\mu\vec b\).

Conditions: \(\vec b\neq \vec 0\).

Distance between two parallel lines in space.