Question

A straight line is equally inclined to all the three coordinate axes. Then, an angle made by the line with the $y$ -axis is

• A. ${\cos }^{-1}\left(\frac{1}{3}\right)$
• B. ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• C. ${\cos }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (B)

Since, a line is equally inclined to the coordinate axes.
$\therefore l=m=n$
$\because l^2+m^2+n^2=1$
$\Rightarrow 3l^2=1$
$\Rightarrow l=\pm \frac{1}{\sqrt{3}}$
$\therefore$ Angle made by line with $y$ -axis $={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$