$\begin{aligned} & \overrightarrow{\mathrm{AM}} \cdot(2 \hat{\imath}+3 \hat{\jmath}+5 \hat{k})=0 \\ & (2 \lambda-7)(2)+(3 \lambda-6)(3)+(5 \lambda-5)(5)=0 \\ & 38 \lambda=57 \\ & \lambda=\frac{3}{2}\end{aligned}$
$\begin{aligned} & \mathrm{M}\left(4, \frac{7}{2}, \frac{19}{2}\right) \\ & \mathrm{A}^{\prime}(0,2,12)\end{aligned}$