VT = \[\overrightarrow {AD} + \overrightarrow {BE} + \overrightarrow {CF} \]

\[ = \overrightarrow {AE} + \overrightarrow {ED} + \overrightarrow {BF} + \overrightarrow {FE} + \overrightarrow {CD} + \overrightarrow {DF} \]

\[ = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} + \left( {\overrightarrow {ED} + \overrightarrow {DF} } \right) + \overrightarrow {FE} \]

\[ = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} + \left( {\overrightarrow {EF} + \overrightarrow {FE} } \right)\]

\[ = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} + \overrightarrow {EE} \]

\[ = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} \](do \[\overrightarrow {EE} = \overrightarrow 0 \]) = VP

Vậy \[\overrightarrow {AD} + \overrightarrow {BE} + \overrightarrow {CF} = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} \].