Direction cosines from direction ratios for JEE

Formula

\(l=\pm\frac{a}{\sqrt{a^2+b^2+c^2}},\quad m=\pm\frac{b}{\sqrt{a^2+b^2+c^2}},\quad n=\pm\frac{c}{\sqrt{a^2+b^2+c^2}}\)

Variables: \((a,b,c)\) are direction ratios; \((l,m,n)\) are corresponding direction cosines.

Conditions: Signs are taken consistently so that \((l:m:n)=(a:b:c)\).

Converting d.r.s to unit direction data; line-angle questions.