A) \[l=m=n=\frac{1}{\sqrt{3}}\]
B) \[l=m=n=\pm \frac{1}{\sqrt{3}}\]
C) \[l=m=n=-\frac{1}{\sqrt{3}}\]
D) \[l=m=n=\pm \frac{1}{\sqrt{2}}\]
Correct Answer: A
Solution :
Since, the line makes an equal angle to the coordinate axes i. e., \[(\alpha =\beta =\gamma )\] As we know, \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\Rightarrow \]\[3{{\cos }^{2}}\alpha =1\]\[\Rightarrow \]\[{{\cos }^{2}}\alpha =\frac{1}{3}\] \[\Rightarrow \]\[\cos \alpha =\pm \frac{1}{\sqrt{3}}\] Since the line lies in the OXYZ octant, so we take \[\text{+}\,\text{ve}\] sign \[\therefore \] \[l=m=n=\frac{1}{\sqrt{3}}\]
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