A) \[\frac{12}{29},\frac{4}{29},\frac{13}{29}\]
B) \[\frac{12}{139},\frac{4}{\sqrt{329}},\frac{13}{\sqrt{329}}\]
C) \[\frac{1}{12},\frac{1}{4},\frac{1}{13}\]
D) \[\frac{12}{329},\frac{4}{329},\frac{13}{329}\]
E) \[\frac{12}{13},\frac{4}{13},1\]
Correct Answer: B
Solution :
Let AB be the given line and the DCs of AB are\[l,m,n.\] Then, \[AB.l=12\] \[AB.m=4\] \[AB.n=13\] On squaring and adding both sides, we get \[A{{B}^{2}}({{l}^{2}}+{{m}^{2}}+{{n}^{2}})=144+16+169=329\] \[AB=\sqrt{329}\] \[\therefore \]DCs of AB are\[12/\sqrt{329},4/\sqrt{329},12/\sqrt{329}\]
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