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

Answers (1)

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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