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D.C’s of a line are proportional to $(1, - 2, 1)$ then d.c’s are

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$(1, - 2, 1)$

$\pm (\frac{1}{\sqrt{6}}, \frac{- 2}{\sqrt{6}}, \frac{1}{\sqrt{6}})$

$\pm (\frac{1}{\sqrt{3}}, \frac{- 2}{\sqrt{3}}, \frac{1}{\sqrt{3}})$

$(1, 2, - 1)$

answer is C.

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Detailed Solution

$(a, b, c) = (1, - 2, 1)$

$\Rightarrow (l, m, n) = \pm \frac{(a, b, c)}{\sqrt{a^{2} + b^{2} + c^{2}}}$

$= \pm \frac{(1, - 2, 1)}{\sqrt{6}}$

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