Question

Cho hình bình hành ABCD tâm O, M là điểm bất kì. CMR: \(\overrightarrow{BA}+\overrightarrow{BC}+\overrightarrow{OB}=\overrightarrow{MO}-\overrightarrow{MB}\)

Answer 1

Ta có :

\(\overrightarrow{BA}+\overrightarrow{BC}+\overrightarrow{OB}=\overrightarrow{MO}-\overrightarrow{MB}\)

\(\Leftrightarrow\overrightarrow{BA}+\overrightarrow{BC}+\overrightarrow{OB}=\overrightarrow{BO}\)

\(\Leftrightarrow\overrightarrow{BA}+\overrightarrow{OC}=\overrightarrow{BO}\)

\(\Leftrightarrow\overrightarrow{BA}+\overrightarrow{AO}=\overrightarrow{BO}\)

\(\Leftrightarrow\overrightarrow{BO}=\overrightarrow{BO}\) ( đpcm )