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

 

 

 

 

 
 
 
 
 

Answers (1)

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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