If $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$ are direction cosines of a line, then the values of c are _______________.

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Solution

Let us suppose $l = \frac{1}{c}, m = \frac{1}{c} and n = \frac{1}{c}$ be the given direction cosines of a line
$i . e l^{2} + m^{2} + n^{2} = 1 i . e {(\frac{1}{c})}^{2} + {(\frac{1}{c})}^{2} + {(\frac{1}{c})}^{2} = 1 i . e \frac{1}{c^{2}} + \frac{1}{c^{2}} + \frac{1}{c^{2}} = 1 i . e 3 \times \frac{1}{c^{2}} = 1 i . e c^{2} = 3 i . e c = \pm \sqrt{3}$

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