Cho 6 điểm A, B, C, D, E, F. Chứng minh rằng: vecto AB + vecto CD + vecto EF

Ta có :

\(\overrightarrow {AB} + \overrightarrow {CD} + \overrightarrow {EF} = \overrightarrow {AD} + \overrightarrow {DB} + \overrightarrow {CF} + \overrightarrow {FD} + \overrightarrow {EB} + \overrightarrow {BF} \)

\( = (\overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {CF} ) + (\overrightarrow {FD} + \overrightarrow {DB} + \overrightarrow {BF} ) = \overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {CF} + \overrightarrow {FF} \)

\( = \overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {CF} + \overrightarrow 0 = \overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {CF} \)

Vậy \(\overrightarrow {AB} + \overrightarrow {CD} + \overrightarrow {EF} = \overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {CF} \).