Lời giải:\(\begin{array}{l}
\overrightarrow {AB} .\overrightarrow {CD} + \overrightarrow {AC} .\overrightarrow {DB} + \overrightarrow {AD} .\overrightarrow {BC} = \left( {\overrightarrow {AC} + \overrightarrow {CB} } \right).\overrightarrow {CD} + \overrightarrow {AC} .\overrightarrow {DB} - \overrightarrow {AD} .\overrightarrow {CB} \\
= \overrightarrow {AC} \left( {\overrightarrow {CD} + \overrightarrow {DB} } \right) + \overrightarrow {CB} \left( {\overrightarrow {CD} - \overrightarrow {AD} } \right) = \overrightarrow {AC} .\overrightarrow {CB} + \overrightarrow {CB} .\overrightarrow {AC} = 0.
\end{array}\)
