Đáp án:
$\begin{array}{l}
a)\overrightarrow {DE} = \overrightarrow {DA} + \overrightarrow {AE} \\
\Rightarrow \overrightarrow {DE} = - 2.\overrightarrow {AB} + \frac{2}{3}.\overrightarrow {AC} \left( {dpcm} \right)\\
b) + )\overrightarrow {DM} = \overrightarrow {DB} + \overrightarrow {BM} \\
\Rightarrow \overrightarrow {DM} = - \overrightarrow {AB} + \frac{1}{2}.\overrightarrow {BC} = - \overrightarrow {AB} - \frac{1}{2}\overrightarrow {AB} + \frac{1}{2}\overrightarrow {AC} \\
\Rightarrow \overrightarrow {DM} = - \frac{3}{2}\overrightarrow {AB} + \frac{1}{2}\overrightarrow {AC} = \frac{{ - 3\overrightarrow {AB} + \overrightarrow {AC} }}{2}\\
\Rightarrow \overrightarrow {DM} = \frac{2}{3}\overrightarrow {DE}
\end{array}$
Vậy D,E,M thẳng hàng
