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If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$, then $c$ is equal to
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$\pm \sqrt{3}$
Direction cosine of line is $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$.
$\therefore \quad \frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1$
$\Rightarrow \quad \frac{3}{c^2}=1 \Rightarrow c^2=3$
$\therefore \quad c= \pm \sqrt{3}$
$\therefore \quad \frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1$
$\Rightarrow \quad \frac{3}{c^2}=1 \Rightarrow c^2=3$
$\therefore \quad c= \pm \sqrt{3}$
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