Question

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

Answer 1

Let angles made by line cos

coordinate axes be $\alpha ,\beta ,\gamma$

$\therefore \alpha =\beta =\gamma \Rightarrow$ (Given)

We know that,

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1\to$ Property

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

$\therefore 3{\cos }^2\alpha =1$

$\therefore {\cos }^2\alpha =\frac{1}{3}$

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

$\therefore$ direction cosines are $(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}})$

OR

$(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{3}})$