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a: \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{DE}\)
\(=\overrightarrow{AC}+\overrightarrow{CD}+\overrightarrow{DE}\)
\(=\overrightarrow{AC}+\overrightarrow{CE}=\overrightarrow{AE}\)
b: \(\overrightarrow{AC}+\overrightarrow{BE}+\overrightarrow{CB}+\overrightarrow{DA}\)
\(=\overrightarrow{AC}+\overrightarrow{CB}+\overrightarrow{BE}+\overrightarrow{DA}=\overrightarrow{AB}+\overrightarrow{BE}+\overrightarrow{DA}\)
\(=\overrightarrow{DA}+\overrightarrow{AE}=\overrightarrow{DE}\)
c: \(\overrightarrow{AB}+\overrightarrow{DC}+\overrightarrow{BD}+\overrightarrow{CA}\)
\(=\overrightarrow{AB}+\overrightarrow{BD}+\overrightarrow{DC}+\overrightarrow{CA}\)
\(=\overrightarrow{AD}+\overrightarrow{DA}=\overrightarrow{0}\)
d: \(\overrightarrow{BC}+\overrightarrow{AD}+\overrightarrow{CD}+\overrightarrow{DA}\)
\(=\overrightarrow{AD}+\overrightarrow{BC}+\overrightarrow{CA}=\overrightarrow{AD}+\overrightarrow{BA}=\overrightarrow{BD}\)
a) ta có : \(\overrightarrow{AB}-\overrightarrow{CD}=\overrightarrow{AB}+\overrightarrow{DC}=\overrightarrow{AP}+\overrightarrow{PQ}+\overrightarrow{QB}+\overrightarrow{DP}+\overrightarrow{PQ}+\overrightarrow{QC}\)
\(=2\overrightarrow{PQ}+\left(\overrightarrow{AP}+\overrightarrow{DP}\right)+\left(\overrightarrow{QB}+\overrightarrow{QC}\right)=2\overrightarrow{PQ}\) ..................(1)
\(\overrightarrow{AC}-\overrightarrow{BD}=\overrightarrow{AC}+\overrightarrow{DB}=\overrightarrow{AP}+\overrightarrow{PQ}+\overrightarrow{QC}+\overrightarrow{DP}+\overrightarrow{PQ}+\overrightarrow{QB}\)\(=2\overrightarrow{PQ}+\left(\overrightarrow{AP}+\overrightarrow{DP}\right)+\left(\overrightarrow{QB}+\overrightarrow{QC}\right)=2\overrightarrow{PQ}\) ..................(2)
từ (1) và (2) ta có : \(\overrightarrow{AB}-\overrightarrow{CD}=\overrightarrow{AC}-\overrightarrow{BD}=2\overrightarrow{PQ}\left(đpcm\right)\)