If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are the direction ratios of a line $\mathrm{L}$ and $\ell, m, n$ are…
If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are the direction ratios of a line $\mathrm{L}$ and $\ell, m, n$ are its direction cosines, then $\frac{a^2}{b^2+c^2}=$
$\frac{1-\ell^2}{\ell^2}$
$\frac{\ell^2}{1+\ell^2}$
$\frac{\ell^2}{\ell^2+m^2}$
$\frac{\ell^2}{1-\ell^2}$
Solution
Let $\mathrm{a}=\frac{1}{\mathrm{k}}, \mathrm{b}=\frac{\mathrm{m}}{\mathrm{k}}$ and $\mathrm{c}=\frac{\mathrm{n}}{\mathrm{k}}$
$
\begin{aligned}
& \Rightarrow \frac{\mathrm{a}^2}{\mathrm{~b}^2+\mathrm{c}^2}=\frac{\mathrm{l}^2}{\mathrm{~m}^2+\mathrm{n}^2} \\
& =\frac{\mathrm{l}^2}{1-\mathrm{p}^2}\left[\because 1^2+\mathrm{m}^2+\mathrm{n}^2=1\right]
\end{aligned}
$