Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
\overrightarrow {CI} = \overrightarrow {AI} - \overrightarrow {AC} = \overrightarrow {AG} + \overrightarrow {GI} - \overrightarrow {AC} = \frac{2}{3}\overrightarrow {AM} + \overrightarrow {BG} - \overrightarrow {AC} \\
= \frac{2}{3}\overrightarrow {AB} + \frac{2}{3}\overrightarrow {BM} + \overrightarrow {AG} - \overrightarrow {AB} - \overrightarrow {AC} \\
= \frac{2}{3}\overrightarrow {AB} + \frac{2}{3}\overrightarrow {BM} + \frac{2}{3}\overrightarrow {AM} - \overrightarrow {AB} - \overrightarrow {AC} \\
= \frac{2}{3}\overrightarrow {AB} + \frac{2}{3}\overrightarrow {BM} + \frac{2}{3}\overrightarrow {AC} + \frac{2}{3}\overrightarrow {CM} - \overrightarrow {AB} - \overrightarrow {AC} \\
= \frac{{ - 1}}{3}\overrightarrow {AB} - \frac{1}{3}\overrightarrow {AC} + \frac{2}{3}(\overrightarrow {BM} + \overrightarrow {CM} )\\
= \frac{{ - 1}}{3}\overrightarrow {AB} - \frac{1}{3}\overrightarrow {AC} + \overrightarrow 0 = \frac{{ - 1}}{3}\overrightarrow {AB} - \frac{1}{3}\overrightarrow {AC}
\end{array}\)
