Question

The direction cosine of a line equally inclined to the axes are

• A. $\frac{1}{3},\frac{1}{3},\frac{1}{3}$
• B. $-\frac{1}{3},-\frac{1}{3},-\frac{1}{3}$
• C. $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$
• D. none of these

Answer 1

The correct option is C $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$

If $a$ line makes angles $\alpha ,\beta ,\gamma$ with the axes, we have $\alpha =\beta =\gamma$

$\therefore \cos \alpha =\cos \beta =\cos \gamma \Rightarrow l=m=n$

$\because l^2+m^2+n^2=1$

$\Rightarrow l^2+l^2+l^2$

$\Rightarrow {3l}^2=1$

$\Rightarrow l^2=\frac{1}{3}$

$\Rightarrow l=\pm \frac{1}{\sqrt{3}}$