A) \[\pi \]
B) \[\pi /3\]
C) \[\pi /4\]
D) \[\pi /6\]
Correct Answer: B
Solution :
If \[l,m,n\]are direction cosines of two lines are such that \[l+m+n=0\] ...(i) and \[{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\] ?(ii) \[\Rightarrow \]\[{{l}^{2}}+{{m}^{2}}-{{(-1-m)}^{2}}=0\] \[\Rightarrow \]\[2\,lm=0\] \[\Rightarrow \]\[l=0\]or \[m=0\] If \[l=0,\]then\[n=-m\] \[\Rightarrow \] \[l:m:n=0:1:-1\] and if \[m=0,\]then\[n=-1\] \[\Rightarrow \]\[l:m:n=1:0:-1\] \[\therefore \] \[\cos \theta =\frac{0+0+1}{\sqrt{0+1+1}\sqrt{0+1+1}}=\frac{1}{2}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\]
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