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

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

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If the line is making equal angle with the coordinate axes. Then,

Let the common angle made is \alpha with each coordinate axes.

Therefore, we can write;

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

And as we know the relation; l^2+m^2+n^2 = 1

\Rightarrow \cos^2 \alpha +\cos^2 \alpha+\cos^2 \alpha = 1

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

or \cos \alpha =\pm \frac{1}{\sqrt3}

Thus the direction cosines of the line are \pm \frac{1}{\sqrt3},\ \pm \frac{1}{\sqrt3},and\ \pm \frac{1}{\sqrt3}  .

 

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