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

The correct option is B ${\cos }^1\left(\frac{1}{\sqrt{3}}\right)$

Let $l,m,n$ be the directional cosines of the line.

We know that $l^2+m^2+n^2=1$

Since the line is equally inclined to all the axes, $l=m=n$

Solving the two above equations we get, $l=m=n=\frac{1}{\sqrt{3}}$

Hence the angle made be the line with any axis is,

$co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$