Vì M thuộc đường thẳng d nên $M\left( 1+3m;2-m;1+m \right)$

$d\left( M,\left( P \right) \right)=\frac{\left| 2\left( 1+3m \right)-2\left( 2-m \right)+1+m+1 \right|}{\sqrt{{{2}^{2}}+{{2}^{2}}+{{1}^{2}}}}=\frac{\left| 9m \right|}{3}$

Theo bài ra ta có

$d\left( M,\left( P \right) \right)=3\to \frac{\left| 9m \right|}{3}=3\to \left[ \begin{align} & m=1 \\ & m=-1 \\ \end{align} \right.$$\to \left[ \begin{align} & M\left( 4;1;2 \right) \\ & M\left( -2;3;0 \right) \\ \end{align} \right.$