Question

# If the direction cosines of line are $$\displaystyle\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$$, then.

A
0<c<1
B
c>2
C
c>0
D
c=±3

Solution

## The correct option is D $$c =\pm \sqrt{3}$$Given that the direction cosines of a line are $$\dfrac {1}{c}, \dfrac {1}{c}, \dfrac {1}{c}$$.We know the sum of the squares of the direction cosines is one.i.e. $$\left(\dfrac {1}{c}\right)^2+\left (\dfrac {1}{c}\right)^2+\left (\dfrac {1}{c}\right)^2=1$$$$\Rightarrow \dfrac {3}{c^2}=1$$$$\Rightarrow c^2=3$$$$\Rightarrow c=\pm \sqrt 3$$Maths

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