\(\begin{array}{l}\overrightarrow {OA} + \overrightarrow {OB} + \overrightarrow {OC} + \overrightarrow {OD} = \left( {\overrightarrow {OA} + \overrightarrow {OB} } \right) + \left( {\overrightarrow {OC} + \overrightarrow {OD} } \right)\\ = 2\overrightarrow {OE} + 2\overrightarrow {OF} = 2\left( {\overrightarrow {OE} + \overrightarrow {OF} } \right) = 2.\overrightarrow 0 = \overrightarrow 0 \end{array}\)