Lời giải chi tiết:

\(\begin{array}{l}
1.\,\,\overrightarrow {AD} + \overrightarrow {BE} + \overrightarrow {CF} \\
= \overrightarrow {AE} + \overrightarrow {ED} + \overrightarrow {BF} + \overrightarrow {FE} + \overrightarrow {CD} + \overrightarrow {DF} \\
= \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} + \left( {\overrightarrow {ED} + \overrightarrow {DF} + \overrightarrow {FE} } \right)\\
= \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} \,\,\,\left( {do\,\,\overrightarrow {ED} + \overrightarrow {DF} + \overrightarrow {FE} = \overrightarrow {EE} = \overrightarrow 0 \,} \right)\\
2.\,\,\overrightarrow {AB} + \overrightarrow {CD} = \left( {\overrightarrow {AD} + \overrightarrow {DB} } \right) + \left( {\overrightarrow {CB} + \overrightarrow {BD} } \right)\\
= \overrightarrow {AD} + \overrightarrow {CB} + \left( {\overrightarrow {DB} + \overrightarrow {BD} } \right)\\
= \overrightarrow {AD} + \overrightarrow {CB} \,\,\,\left( {do\,\,\,\overrightarrow {DB} + \overrightarrow {BD} = \overrightarrow 0 } \right).\\
3.\,\,\overrightarrow {AB} - \overrightarrow {CD} = \left( {\overrightarrow {AC} + \overrightarrow {CB} } \right) - \left( {\overrightarrow {CB} + \overrightarrow {BD} } \right)\\
= \overrightarrow {AC} - \overrightarrow {BD} + \left( {\overrightarrow {CB} - \overrightarrow {CB} } \right)\\
= \overrightarrow {AC} - \overrightarrow {BD} .
\end{array}\)