A straight line is equally inclined to all th | vedclass

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(B) Let the direction cosines of the line be $(l, m, n)$. Since the line is equally inclined to the coordinate axes,the angles made by the line with t

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

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(B) Let the direction cosines of the line be $(l, m, n)$. Since the line is equally inclined to the coordinate axes,the angles made by the line with the $x, y,$ and $z$-axes are equal. Let this angle be $\alpha$.Thus,$l = \cos \alpha, m = \cos \alpha, n = \cos \alpha$.We know that for any line,the sum of the squares of the direction cosines is $1$,i.e.,$l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.$3 \cos^2 \alpha = 1$.$\cos^2 \alpha = \frac{1}{3}$.$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.Since the angle $\alpha$ is the angle with the $y$-axis,$\cos \alpha = \frac{1}{\sqrt{3}}$ (taking the positive value for the acute angle).Therefore,$\alpha = \cos^{-1}\left(\frac{1}{\sqrt{3}}\right)$.

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

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