A) \[\frac{1}{3},\frac{1}{3},\frac{1}{3}\]
B) \[\frac{-1}{3},\frac{-1}{3},\frac{-1}{3}\]
C) \[\pm \frac{1}{2},\pm \frac{1}{2},\pm \frac{1}{2}\]
D) \[\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}}\]
Correct Answer: D
Solution :
[d] Let l, m and n be the direction cosine of a line. \[\therefore {{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1\] According to question, \[{{l}^{2}}={{m}^{2}}={{n}^{2}}\] \[\Rightarrow 3{{l}^{2}}=1\Rightarrow {{l}^{2}}=\frac{1}{3}\] Thus, the d.c. of a line be \[\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}}\] Hence, option [d] is correct.
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