A) 2
B) 4
C) 6
D) 8
Correct Answer: B
Solution :
Since \[\alpha =\beta =\gamma \,\,\,\Rightarrow \,\,{{\cos }^{2}}\alpha +{{\cos }^{2}}\alpha +{{\cos }^{2}}\alpha =1\] \[\Rightarrow \,\,\alpha ={{\cos }^{-1}}\left( \pm \,\frac{1}{\sqrt{3}} \right)\] So, there are four lines whose direction cosines are \[\left( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right),\,\left( \frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right),\,\left( \frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right),\] \[\left( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}} \right)\].
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