\[\begin{array}{l}
3\overrightarrow {MA} + 4\overrightarrow {MB} = \overrightarrow 0 \Leftrightarrow 3\overrightarrow {MA} + 4\left( {\overrightarrow {MA} + \overrightarrow {AB} } \right) = \overrightarrow 0 \\
\Leftrightarrow 7\overrightarrow {MA} = - 4\overrightarrow {AB} \Leftrightarrow 7\overrightarrow {AM} = 4\overrightarrow {AB} \Leftrightarrow \overrightarrow {AM} = \frac{4}{7}\overrightarrow {AB} \\
\overrightarrow {NB} - 3\overrightarrow {NC} = \overrightarrow 0 \Leftrightarrow \overrightarrow {AB} - \overrightarrow {AN} - 3\left( {\overrightarrow {AC} - \overrightarrow {AN} } \right) = \overrightarrow 0 \\
\Leftrightarrow - 4\overrightarrow {AN} + \overrightarrow {AB} - 3\overrightarrow {AC} = \overrightarrow 0 \Leftrightarrow \overrightarrow {AN} = \frac{1}{4}\overrightarrow {AB} - \frac{3}{4}\overrightarrow {AC} \\
\overrightarrow {AG} = \frac{1}{3}\left( {\overrightarrow {AA} + \overrightarrow {AB} + \overrightarrow {AC} } \right) = \frac{1}{3}\overrightarrow {AB} + \frac{1}{3}\overrightarrow {AC} \\
Ta\,co:\\
\overrightarrow {MN} = \overrightarrow {AN} - \overrightarrow {AM} = \frac{1}{4}\overrightarrow {AB} - \frac{3}{4}\overrightarrow {AC} - \frac{4}{7}\overrightarrow {AB} = - \frac{9}{{28}}\overrightarrow {AB} - \frac{3}{4}\overrightarrow {AC} \\
\overrightarrow {MG} = \overrightarrow {AG} - \overrightarrow {AM} = \frac{1}{3}\overrightarrow {AB} + \frac{1}{3}\overrightarrow {AC} - \frac{4}{7}\overrightarrow {AB} = - \frac{5}{{21}}\overrightarrow {AB} + \frac{1}{3}\overrightarrow {AC} \\
\Rightarrow 3\,diem\,M,N,G\,khong\,thang\,hang\\
\Rightarrow Xem\,lai\,de\,bai
\end{array}\]
