Question

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

• A. $0<c<1$
• B. $c>2$
• C. $c=\pm \sqrt{2}$
• D. $c=\pm \sqrt{3}$
• E. $c=\pm 3$

Answer 1

Answer: (D)

Since, DCs of a line are $\left(\frac{1}{c},\frac{1}{c},\frac{1}{c}\right)$ .
$\therefore$ ${\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2+{\left(\frac{1}{c}\right)}^2=1$
$\Rightarrow$ $c^2=3\Rightarrow c=\pm \sqrt{3}$