\[\begin{array}{l}
+ )\,\,\,\overrightarrow {AI} = \frac{1}{2}\left( {\overrightarrow {AO} + \overrightarrow {AB} } \right) = \frac{1}{2}\overrightarrow {AO} + \frac{1}{2}\overrightarrow {AB} \\
= \frac{1}{2}.\frac{1}{2}\overrightarrow {AC} + \frac{1}{2}\overrightarrow {AB} = \frac{1}{4}\left( {\overrightarrow {AB} + \overrightarrow {AD} } \right) + \frac{1}{2}\overrightarrow {AB} \\
= \frac{1}{4}\overrightarrow {AB} + \frac{1}{4}\overrightarrow {AD} + \frac{1}{2}\overrightarrow {AB} = \frac{3}{4}\overrightarrow {AB} + \frac{1}{4}\overrightarrow {AD} .\\
+ )\,\,\overrightarrow {BG} = \overrightarrow {BO} + \overrightarrow {OG} = \frac{1}{2}\left( {\overrightarrow {BA} + \overrightarrow {BC} } \right) + \frac{2}{3}\overrightarrow {OM} \,\,\left( {\,M\,\,\,la\,\,\,\,trung\,\,diem\,\,cua\,\,DC} \right)\\
= \frac{1}{2}\overrightarrow {BA} + \frac{1}{2}\overrightarrow {BC} + \frac{2}{3}.\frac{1}{2}\overrightarrow {AD} = - \frac{1}{2}\overrightarrow {AB} + \frac{1}{2}\overrightarrow {AD} + \frac{1}{3}\overrightarrow {AD} \\
= - \frac{1}{2}\overrightarrow {AB} + \frac{5}{6}\overrightarrow {AD} .
\end{array}\]
\[\begin{array}{l}
+ )\,\,\,\overrightarrow {IG} = \overrightarrow {IO} + \overrightarrow {OG} = \frac{1}{2}\overrightarrow {BO} + \frac{2}{3}\overrightarrow {OM} \\
= \frac{1}{2}.\frac{1}{2}\left( {\overrightarrow {BA} + \overrightarrow {BC} } \right) + \frac{2}{3}.\frac{1}{2}\overrightarrow {AD} \\
= \frac{1}{4}\overrightarrow {BA} + \frac{1}{4}\overrightarrow {BC} + \frac{1}{3}\overrightarrow {AD} \\
= - \frac{1}{4}\overrightarrow {AB} + \frac{1}{4}\overrightarrow {AD} + \frac{1}{3}\overrightarrow {AD} \\
= - \frac{1}{4}\overrightarrow {AB} + \frac{7}{{12}}\overrightarrow {AD} .
\end{array}\]
