Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\frac{1}{2}\left( {\overrightarrow {AF} + \overrightarrow {AH} - \overrightarrow {AC} } \right)\\
= \frac{1}{2}\left( {\overrightarrow {AE} + \overrightarrow {EF} + \overrightarrow {AE} + \overrightarrow {EH} - \overrightarrow {AC} } \right)\\
= \frac{1}{2}\left( {2\overrightarrow {AE} + \left( {\overrightarrow {EF} + \overrightarrow {EH} } \right) - \overrightarrow {AC} } \right)\\
= \frac{1}{2}\left( {2\overrightarrow {AE} + \overrightarrow {EG} - \overrightarrow {EG} } \right)\\
= \frac{1}{2}.2\overrightarrow {AE} = \overrightarrow {AE} \\
b,\\
\frac{1}{2}\left( {\overrightarrow {AF} + \overrightarrow {AH} + \overrightarrow {AC} } \right)\\
= \frac{1}{2}\left( {\overrightarrow {AE} + \overrightarrow {EF} + \overrightarrow {AE} + \overrightarrow {EH} + \overrightarrow {AC} } \right)\\
= \frac{1}{2}\left( {2\overrightarrow {AE} + \left( {\overrightarrow {EF} + \overrightarrow {EH} } \right) + \overrightarrow {AC} } \right)\\
= \frac{1}{2}.\left( {2\overrightarrow {AE} + \overrightarrow {EG} + \overrightarrow {EG} } \right)\\
= \overrightarrow {AE} + \overrightarrow {EG} = \overrightarrow {AG}
\end{array}\)
