Direction cosines of a vector for JEE

Formula

\(l=\dfrac{a_x}{|\vec{a}|},\quad m=\dfrac{a_y}{|\vec{a}|},\quad n=\dfrac{a_z}{|\vec{a}|}\)

Variables: \(l,m,n\) are direction cosines of \(\vec{a}=a_x\hat{i}+a_y\hat{j}+a_z\hat{k}\).

Conditions: \(\vec{a}\neq \vec{0}\).

Angles with coordinate axes, unit direction vectors.