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If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$ then
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The correct answer is:
$\mathrm{c}=\pm \sqrt{3}$
Given $\ell=m=n=\frac{1}{c}$
We know that $\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \Rightarrow \frac{3}{\mathrm{c}^{2}}=1 \Rightarrow \mathrm{c}^{2}=3 \Rightarrow \mathrm{c}=\pm \sqrt{3}$
We know that $\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \Rightarrow \frac{3}{\mathrm{c}^{2}}=1 \Rightarrow \mathrm{c}^{2}=3 \Rightarrow \mathrm{c}=\pm \sqrt{3}$
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