Question

cho 6 điểm a b c d e f chứng minh vecto AC+ vecto BD+ vecto EF=vecto AF+ vecto BC+ vecto ED

Answer 1

Chuyển vế: \(\overrightarrow{AC}+\overrightarrow{BD}+\overrightarrow{EF}-\overrightarrow{AF}-\overrightarrow{BC}-\overrightarrow{ED}\)\(=\overrightarrow{AC}+\overrightarrow{BD}+\overrightarrow{EF}+\overrightarrow{FA}+\overrightarrow{CB}+\overrightarrow{DE}\)\(=\left(\overrightarrow{AC}+\overrightarrow{CB}\right)+\left(\overrightarrow{BD}+\overrightarrow{DE}\right)+\left(\overrightarrow{EF}+\overrightarrow{FA}\right)\)\(=\overrightarrow{AB}+\overrightarrow{BE}+\overrightarrow{EA}\)\(=\overrightarrow{AE}+\overrightarrow{EA}\)

\(=0\)

Suy ra: \(\overrightarrow{AC}+\overrightarrow{BD}+\overrightarrow{EF}=\overrightarrow{AF}+\overrightarrow{BC}+\overrightarrow{ED}\)