$$\begin{aligned} &\begin{aligned} & \overrightarrow{\mathrm{PQ}} \perp(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \\ & \Rightarrow 2(2 \lambda-3)+1(\lambda-2)+3(3 \lambda-2)=0 \\ & \Rightarrow 14 \lambda-14=0, \lambda=1 \\ & \text { So, } \mathrm{Q}(3,3,4) \end{aligned}\\ &\text { Let image in } R(\alpha, \beta, \gamma)\\ &\begin{aligned} & \frac{\alpha+4}{2}=3, \frac{\beta+4}{2}=3, \frac{\gamma+3}{2}=4 \\ & (\alpha, \beta, \gamma)=(2,2,5) \\ & \Rightarrow \alpha+\beta+\gamma=9 \end{aligned} \end{aligned}$$