Cho 6 điểm A, B, C, D, E, F. Chứng minh rằng

\(\overrightarrow {AD} + \overrightarrow {BE} + \overrightarrow {CF} = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} = \overrightarrow {AF} + \overrightarrow {BD} + \overrightarrow {CE} \).

\(\overrightarrow {AD} + \overrightarrow {BE} + \overrightarrow {CF} = \overrightarrow {AE} + \overrightarrow {ED} + \overrightarrow {BF} + \overrightarrow {FE} + \overrightarrow {CD} + \overrightarrow {DF} \)

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

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

\( = \overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} \)

Lại có: \(\overrightarrow {AE} + \overrightarrow {BF} + \overrightarrow {CD} = \overrightarrow {AF} + \overrightarrow {FE} + \overrightarrow {BD} + \overrightarrow {DF} + \overrightarrow {CE} + \overrightarrow {ED} \)

\( = \left( {\overrightarrow {AF} + \overrightarrow {BD} + \overrightarrow {CE} } \right) + \left( {\overrightarrow {FE} + \overrightarrow {ED} + \overrightarrow {DF} } \right)\)

\( = \overrightarrow {AF} + \overrightarrow {BD} + \overrightarrow {CE} \).