A) \[-\,3\,\,\le \,\,m\,\,<-1\]
B) \[6\,\,\le \,\,m\,\,<\,\,8\]
C) \[4\,\,\le \,\,m\,\,<\,\,6\]
D) \[2\,\,\le \,\,m\,\,<\,\,4\]
Correct Answer: D
Solution :
\[{{m}_{\text{AB}}}.\,{{m}_{\text{cm}}}\,=\,-\,1\] |
\[\Rightarrow \] \[m.\left( \frac{1\,-\,\frac{3}{5}\,m\,+2}{-\,\frac{3}{5}\,-\,3} \right)\,=\,-1\] |
\[\Rightarrow \] \[m\left( \frac{15-3m}{-\,18}\, \right)\,=\,-1\] |
\[\Rightarrow \] \[15\,-\,3{{m}^{2}}-18\,=\,0\] |
\[\Rightarrow \] \[{{m}^{2}}\,-\,5m\,+\,6\,=\,0\] |
\[M=2,m=3\]\[\Rightarrow \] \[2\le ~m<4.\] |
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