Cho 5 điểm A, B, C, D, E. Chứng minh
a) \(\overrightarrow {AB} + \overrightarrow {CD} + \overrightarrow {EA} = \overrightarrow {CB} + \overrightarrow {ED} \).
b) \(\overrightarrow {AC} + \overrightarrow {CD} - \overrightarrow {EC} = \overrightarrow {AE} - \overrightarrow {DB} + \overrightarrow {CB} \)
a) \(\overrightarrow {AB} + \overrightarrow {CD} + \overrightarrow {EA} = \overrightarrow {EA} + \overrightarrow {AB} + \overrightarrow {CD} = \overrightarrow {EB} + \overrightarrow {CD} \)
\( = \overrightarrow {ED} + \overrightarrow {DB} + \overrightarrow {CB} + \overrightarrow {BD} \)
\( = \overrightarrow {ED} + \overrightarrow {CB} + \overrightarrow {DB} + \overrightarrow {BD} \)
\( = \overrightarrow {ED} + \overrightarrow {CB} + \overrightarrow 0 \)
\( = \overrightarrow {ED} + \overrightarrow {CB} \).
b) \(\overrightarrow {AC} + \overrightarrow {CD} - \overrightarrow {EC} \)
\( = \overrightarrow {AC} + \overrightarrow {CD} + \overrightarrow {CE} \)
\( = \overrightarrow {AE} + \overrightarrow {CD} \)
\( = \overrightarrow {AE} + \overrightarrow {CB} + \overrightarrow {BD} \)
\( = \overrightarrow {AE} + \overrightarrow {CB} - \overrightarrow {DB} \)
\( = \overrightarrow {AE} - \overrightarrow {DB} + \overrightarrow {CB} \).