Q57 / 160 · TS EAMCET 2012 · Mathematics

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

Solution

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

Hence, the correct answer is option: 'B'.

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