$$\begin{aligned} &\text { Let } \mathrm{R}(2 \lambda+1,3 \lambda-1,4 \lambda)\\ &\begin{aligned} & 2 \lambda+1=5 \\ & \lambda=2 \\ & \mathrm{R}(5,5,8) \\ & \text { let } \mathrm{T}(2 \lambda+1,3 \lambda-1,4 \lambda) \\ & \overrightarrow{\mathrm{QT}}=(2 \lambda-6) \hat{\mathrm{i}}+(3 \lambda+1) \hat{\mathrm{j}}+(4 \lambda-5) \hat{\mathrm{k}} \\ & \overrightarrow{\mathrm{~b}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \\ & \overrightarrow{\mathrm{QT}} \cdot \overrightarrow{\mathrm{~b}}=0 \end{aligned}\\ &4 \lambda-12+9 \lambda+3+16 \lambda-20=0 \end{aligned}$$

$$\begin{aligned} & \lambda=1 \\ & \mathrm{~T}(3,2,4) \\ & \mathrm{QT}=\sqrt{33} \quad \mathrm{RT}=\sqrt{29} \\ & (\text { area of } \Delta \mathrm{PQR})^2=\left(\frac{1}{2} \sqrt{29} \cdot 2 \sqrt{33}\right)^2 \\ & =957 \end{aligned}$$