Find the value of λ if the following lines are perpendicular to each other: l_1: (1- x)/-3=(3 y -2)/(2 λ)=(z -3)/3; l_2: (x -1)/(3 λ)=(1- y)/1=(2 z…

$\displaystyle \mathrm{l}_{1}: \frac{\mathrm{x}-1}{3}=\frac{\mathrm{y}-\dfrac{2}{3}}{\dfrac{2}{3} \lambda}=\frac{\mathrm{z}-3}{3}$ \[\mathrm{l}_{2}: \frac{\mathrm{x}-1}{3 \lambda}=\frac{\mathrm{y}-1}{-1}=\frac{\mathrm{z}-\dfrac{5}{2}}{\dfrac{3}{2}} \] lines are perpendicular $\displaystyle \Rightarrow 3(3 \lambda)+\frac{2}{3} \lambda(-1)+3 \cdot \frac{3}{2}=0$ \[\lambda=\frac{-27}{50} \]