Giải thích các bước giải:
$\begin{array}{l}
Do:\frac{{AM}}{{MI}}.\frac{{IB}}{{BC}}.\frac{{CK}}{{KA}} = 1 \Rightarrow \frac{{AM}}{{MI}}.\frac{1}{2}.3 = 1\\
\Rightarrow \frac{{AM}}{{MI}} = \frac{2}{3} \Rightarrow \frac{{AM}}{{AI}} = \frac{2}{5}
\end{array}$
$\begin{array}{l}
\overrightarrow {AM} = \frac{2}{5}\overrightarrow {AI} \\
= \frac{2}{5}.\frac{1}{2}.\left( {\overrightarrow {AB} + \overrightarrow {AC} } \right)\\
= \frac{1}{5}\overrightarrow {AB} + \frac{1}{5}\overrightarrow {AC}
\end{array}$