$\begin{array}{l} a)\overrightarrow {AB} + \overrightarrow {DC} + \overrightarrow {BD} + \overrightarrow {CA} \\ = \left( {\overrightarrow {AB} + \overrightarrow {BD} } \right) + \left( {\overrightarrow {DC} + \overrightarrow {CA} } \right)\\ = \overrightarrow {AD} + \overrightarrow {DA} = \overrightarrow 0 \\ b)\overrightarrow {AB} + \overrightarrow {CD} + \overrightarrow {BC} + \overrightarrow {DA} \\ = \left( {\overrightarrow {CD} + \overrightarrow {DA} } \right) + \left( {\overrightarrow {AB} + \overrightarrow {BC} } \right)\\ = \overrightarrow {CA} + \overrightarrow {AC} = \overrightarrow 0 \end{array}$
