\(\begin{array}{l}
Goi\,\,\,P\left( {a;\,\,b} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\overrightarrow {PM} = \left( {1 - a;\,\,6 - b} \right)\\
\overrightarrow {PN} = \left( {6 - a;\,\,\,3 - b} \right)
\end{array} \right.\\
\Rightarrow \overrightarrow {PM} = 2\overrightarrow {PN} \\
\Leftrightarrow \left( {1 - a;\,\,6 - b} \right) = 2\left( {6 - a;\,\,\,3 - b} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
1 - a = 2\left( {6 - a} \right)\\
6 - b = 2\left( {3 - b} \right)
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
1 - a = 12 - 2a\\
6 - b = 6 - 2b
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 11\\
b = 0
\end{array} \right.\\
\Rightarrow P\left( {11;\,\,0} \right).
\end{array}\)
