A line makes equal angles with coordinate axis. Direction cosines of this line are :

Question

Smart Achievers · Accepted Answer

(2)

Ans. $\pm (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}})$

Explanation:

Let the line make angle $α$ with each of the axis.

Then, its direction cosines are $\cos α, \cos α, \cos α$ .

Since

$\cos^{2} α + \cos^{2} α + \cos^{2} α = 1$

$3 \cos^{2} α = 1$

$\cos^{2} α = \frac{1}{3}$

$∴$ $\cos α = \pm \frac{1}{\sqrt{3}}$

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