Question

If the direction cosines of a line are $(\frac{1}{c},\frac{1}{c},\frac{1}{c})$, then

• A. $0<c<1$
• B. $c>2$
• C. $c=\pm \sqrt{2}$
• D. None of these

Answer 1

The correct option is D None of these

Since, $D{C}^{\prime }s$ of a line are $(\frac{1}{c},\frac{1}{c},\frac{1}{c})$
$\because l^2+m^2+n^2=1$
$\therefore {\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2=1$
$\Rightarrow 1+1+1=c^2\Rightarrow c^2=3$
$\Rightarrow c=\pm \sqrt{3}$.