Question

A line located in a space makes equal angle with the co-ordinate axis then angle makes by line from anyone axis are-

• A. ${60}^0$
• B. ${45}^0$
• C. $co{s}^{-1}1/3$
• D. $co{s}^{-1}1/\sqrt{3}$

Answer 1

The correct option is D $co{s}^{-1}1/\sqrt{3}$

Let the direction cosines of the line make an angle α with each of the coordinate axes.

$l=cos\alpha ,m=cos\alpha ,n=cos\alpha$

$l^2+m^2+n^2=1$

$co{s}^2\alpha +co{s}^2\alpha +co{s}^2\alpha =1$

$3co{s}^2\alpha =1$

$co{s}^2\alpha =\frac{1}{3}$

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$cos\alpha =\pm \frac{1}{\sqrt{3}}$

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

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