Đáp án:
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\overrightarrow {MH} = \overrightarrow {MB} + \overrightarrow {BH} = \frac{1}{2}\overrightarrow {CB} + 2\overrightarrow {BG} = \frac{1}{2}\left( {\overrightarrow {AB} - \overrightarrow {AC} } \right) + \frac{4}{3}\overrightarrow {BN} \\
= \frac{1}{2}\overrightarrow {AB} - \frac{1}{2}\overrightarrow {AC} + \frac{4}{3}.\frac{1}{2}\left( {\overrightarrow {BA} + \overrightarrow {BC} } \right)\\
= \frac{1}{2}\overrightarrow {AB} - \frac{1}{2}\overrightarrow {AC} + \frac{2}{3}\left( { - \overrightarrow {AB} + \overrightarrow {AC} - \overrightarrow {AB} } \right)\\
= \frac{1}{2}\overrightarrow {AB} - \frac{1}{2}\overrightarrow {AC} - \frac{2}{3}\overrightarrow {AB} + \frac{2}{3}\overrightarrow {AC} - \frac{2}{3}\overrightarrow {AB} \\
= - \frac{5}{6}\overrightarrow {AB} + \frac{1}{6}\overrightarrow {AC} = \frac{1}{6}\left( { - 5\overrightarrow {AB} + \overrightarrow {AC} } \right)
\end{array}$
