A) \[\frac{1+3\sqrt{2}}{7}\]
B) \[\frac{1-3\sqrt{2}}{7}\]
C) \[\frac{1\pm 3\sqrt{2}}{7}\]
D) \[\frac{1\pm 5\sqrt{2}}{7}\]
Correct Answer: D
Solution :
\[{{m}_{1}}=3,{{m}_{2}}=\frac{1}{2}\]and \[{{m}_{3}}=m\] Let the angle between first and third line is \[{{\theta }_{1}}\]and between second and third is \[{{\theta }_{2}}\], then \[\tan {{\theta }_{1}}=\frac{3-m}{1+3m}\] and \[\tan {{\theta }_{2}}=\frac{m-\frac{1}{2}}{1+\frac{m}{2}}\] But \[{{\theta }_{1}}={{\theta }_{2}}\Rightarrow \frac{3-m}{1+3m}=\frac{m-\frac{1}{2}}{1+\frac{m}{2}}\] Þ \[7{{m}^{2}}-2m-7=0\]Þ \[m=\frac{1\pm 5\sqrt{2}}{7}\].
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