Ta có :
\(\overrightarrow{BP}+\overrightarrow{AN}+\overrightarrow{CM}=\overrightarrow{BC}+\overrightarrow{CP}+\overrightarrow{AB}+\overrightarrow{BN}+\overrightarrow{CA}+\overrightarrow{AM}=\overrightarrow{CP}+\overrightarrow{BN}+\overrightarrow{AM}\)\(=\dfrac{1}{3}\overrightarrow{AB}+\dfrac{1}{3}\overrightarrow{BC}+\dfrac{1}{3}\overrightarrow{CA}\)
\(=\dfrac{1}{3}\left(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}\right)\)
\(=\dfrac{1}{3}\overrightarrow{0}\)
\(=\overrightarrow{0}\)
\(\RightarrowĐPCM\)