$$\begin{aligned} & \overrightarrow{P A}=(3 \lambda-5) \hat{i}+(2 \lambda-1) \hat{j}+(4 \lambda-3) \hat{k} \\ & (3 \lambda-5) 3+(2 \lambda-1) 2+(4 \lambda-3) 4=0 \\ & \Rightarrow 9 \lambda-15+4 \lambda-2+16 \lambda-12=0 \\ & \Rightarrow 29 \lambda=29 \\ & \therefore \lambda=1 \\ & \therefore \quad A(4,2,6) \\ & \therefore \quad P^{\prime}: \text { mirror image of } P \\ & \Rightarrow P^{\prime}(2,3,7) \\ & \left(O P^{\prime}\right)^2=4+9+49 \\ & =62 \\ & \end{aligned}$$