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  2. Find the direction cosines of a line which makes equal angles with the coordinate axes.          
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Find the direction cosines of a line which makes equal angles with the coordinate axes.

 

 

 

 

 
 
 
 
 

Answers (1)
R Ravindra Pindel

Let the direction cosines of the line make an angle \alpha with each of the coordinate axes and direction cosines can be l, m and n .

\therefore l=\cos \alpha ,\: m=\cos \alpha \:\: and\: \: n=\cos \alpha

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

\therefore \cos ^{2}\alpha +\cos ^{2}\alpha+\cos ^{2}\alpha=1

\Rightarrow 3\cos ^{2}\alpha=1

\Rightarrow \cos ^{2}\alpha=\frac{1}{3}

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

Thus the direction cosines are \left ( \pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}} \right )

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