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Question

If the direction cosines of a line are $$\left (\dfrac {1}{c}, \dfrac {1}{c}, \dfrac {1}{c}\right )$$, then


A
0<c<1
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B
c>2
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C
c=±2
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D
None of these
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Solution

The correct option is D None of these
Since, $$DC's$$ of a line are $$\left (\dfrac {1}{c}, \dfrac {1}{c}, \dfrac {1}{c}\right )$$
$$\because l^{2} + m^{2} + n^{2} = 1$$
$$\therefore \left (\dfrac {1}{c}\right )^{2} + \left (\dfrac {1}{c}\right )^{2} + \left (\dfrac {1}{c}\right )^{2} = 1$$
$$\Rightarrow 1 + 1 + 1 = c^{2} \Rightarrow c^{2} = 3$$
$$\Rightarrow c = \pm \sqrt {3}$$.

Mathematics

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