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A straight line is equally inclined to all the three coordinate axes. Then, an angle made by the line with the $y$-axis is
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Verified Answer
The correct answer is:
$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
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 $=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$\begin{array}{ll}\therefore & l-m=n \\ \because & l^2+m^2+n^2=1 \\ \Rightarrow & 3 l^2=1 \\ \Rightarrow & l= \pm \frac{1}{\sqrt{3}}\end{array}$
$\therefore$ Angle made by line with $y$-axis $=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
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