Vector form of a line for JEE

Formula

\(\vec r=\vec a+\lambda\vec b\)

Variables: \(\vec a\) is position vector of a fixed point on the line, \(\vec b\) is a vector parallel to the line, \(\lambda\in\mathbb{R}\).

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

Compact representation of lines; vector methods in shortest distance problems.