Can $\frac{2}{\sqrt{3}}, \frac{- 2}{\sqrt{3}}, \frac{- 1}{\sqrt{3}}$ be the direction ratios of any directed line? Justify your answer.

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Solution

$\frac{2}{\sqrt{3}}, \frac{- 2}{\sqrt{3}}, \frac{- 1}{\sqrt{3}}$
$= \sqrt{\frac{4}{3} + \frac{4}{\sqrt{3}} + \frac{1}{3}} = \sqrt{3}$ No

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