a) *\(\displaystyle \overrightarrow {AO} = {1 \over 2}\overrightarrow {AC} = {1 \over 2}\overrightarrow {A'C'} \) \(\displaystyle = {1 \over 2}\left( {\overrightarrow {AB} + \overrightarrow {A{\rm{D}}} } \right)\)
\(\displaystyle \overrightarrow {AO} = \overrightarrow {AB} + \overrightarrow {BO} = \overrightarrow {AB} + {1 \over 2}\overrightarrow {B{\rm{D}}} ,....\)
*\(\displaystyle \overrightarrow {AO} = {1 \over 2}\overrightarrow {AC} + \overrightarrow {AA'} \)
\(\displaystyle \eqalign{
& = {1 \over 2}\left( {\overrightarrow {AA'} + \overrightarrow {AC'} } \right) = {1 \over 2}\left( {\overrightarrow {AB'} + \overrightarrow {AD'} } \right) \cr
& = \overrightarrow {AA'} + \overrightarrow {A'B'} + {1 \over 2}\overrightarrow {B'D'} \cr
& = \overrightarrow {AB} + \overrightarrow {BB'} + {1 \over 2}\overrightarrow {B'D'} ,... \cr} \)
b) \(\displaystyle \overrightarrow {AD} + \overrightarrow {D'C'} + \overrightarrow {D'A'}\) \(\displaystyle = \overrightarrow {AD} + \overrightarrow {DC} + \overrightarrow {CB} \)
(vì \(\displaystyle \overrightarrow {D'C'} = \overrightarrow {DC} \) và \(\displaystyle \overrightarrow {D'A'} = \overrightarrow {CB} \)) nên \(\displaystyle \overrightarrow {A{\rm{D}}} + \overrightarrow {D'C'} + \overrightarrow {D'A'} = \overrightarrow {AB} \).
