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
B
c>2
C
c=±2
D
None of these

Solution

## The correct option is D None of theseSince, $$DC's$$ 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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