A) \[3x+y-9=0\]
B) \[5x-y-7=0\]
C) \[5x+y-13=0\]
D) \[3x-y-3=0\]
Correct Answer: B
Solution :
Equation of required line is \[{{L}_{1}}+\lambda {{L}_{2}}=0\] \[\Rightarrow \] \[(2x+3y+1)+\lambda (3x-4y-8)=0\] Since, this line passes through the point (2, 3) \[\therefore \] \[(2\times 2+3\times 3+1)+\lambda (3\times 2-4\times 3-8)=0\] \[\Rightarrow \] \[(4+9+1)+\lambda (6-12-8)=0\] \[\Rightarrow \] \[\lambda =\frac{-14}{-14}\] \[\Rightarrow \] \[\lambda =1\] Hence, equation of required line is \[(2x+3y+1)+\lambda (3x-4y-8)=0\] \[\Rightarrow \] \[5x-y-7=0\]
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