Find the equation of a line l_2 which is the mirror image of the line l_1 with respect to line l: x/1=(y -1)/2=(z -2)/3, given that line l_1 passes…

D ratios of the line $\displaystyle l$ i.e. $\displaystyle \dfrac{x}{1} = \dfrac{y-1}{2} = \dfrac{z-2}{3}$ are $\displaystyle 1,\ 2,\ 3$Let coordinates of foot of perpendicular M on line $\displaystyle l$ be $\displaystyle (\lambda,\ 2\lambda + 1,\ 3\lambda + 2)$D.ratios of PM are $\displaystyle \lambda - 1,\ 2\lambda - 5,\ 3\lambda - 1$$\displaystyle 1(\lambda - 1) + 2(2\lambda - 5) + 3(3\lambda - 1) = 0 \quad (\because \text{PM} \perp l)$$\displaystyle \Rightarrow \lambda = 1$Coordinates of M are $\displaystyle (1,\ 3,\ 5)$Since M is midpoint of PQ $\displaystyle \therefore$ Coordinates of Q are $\displaystyle (1,\ 0,\ 7)$Equation of line $\displaystyle l_2$ is $\displaystyle \dfrac{x-1}{1} = \dfrac{y}{2} = \dfrac{z-7}{3}$