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The d.c.'s of a line which is equally inclined to the coordinate axes are

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$(1 / \sqrt{3}, 1 / \sqrt{3}, 1 / \sqrt{3})$

$(3 / 13, 4 / 13, 12 / 13)$

$(1 / 3, 2 / 3, 2 / 3)$

$(2 / 7, 3 / 7, 6 / 7)$

answer is A.

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Detailed Solution

Given $α = β = γ$ and we know that $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \Rightarrow 3 \cos^{2} α = 1 \Rightarrow \cos α = \pm \frac{1}{\sqrt{3}} .$

$∴$ D.c.'s of a line are $(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}) .$

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