Do M, N, P là trung điểm các cạnh đã cho nên:
\(\left\{{}\begin{matrix}\overrightarrow{NA}=\dfrac{1}{2}\overrightarrow{CA}\\\overrightarrow{PB}=\dfrac{1}{2}\overrightarrow{AB}\\\overrightarrow{MC}=\dfrac{1}{2}\overrightarrow{BC}\end{matrix}\right.\) và \(\left\{{}\begin{matrix}\overrightarrow{BP}=\dfrac{1}{2}\overrightarrow{AB}\\\overrightarrow{NC}=\dfrac{1}{2}\overrightarrow{AC}\end{matrix}\right.\)
\(\Rightarrow\overrightarrow{NA}+\overrightarrow{PB}+\overrightarrow{MC}=\dfrac{1}{2}\left(\overrightarrow{CA}+\overrightarrow{AB}+\overrightarrow{BC}\right)=\dfrac{1}{2}\left(\overrightarrow{CB}+\overrightarrow{BC}\right)=\overrightarrow{0}\)
\(\overrightarrow{MC}+\overrightarrow{BP}+\overrightarrow{NC}=\dfrac{1}{2}\left(\overrightarrow{BC}+\overrightarrow{BA}+\overrightarrow{AC}\right)=\dfrac{1}{2}\left(\overrightarrow{BC}+\overrightarrow{BC}\right)=\dfrac{1}{2}.2\overrightarrow{BC}=\overrightarrow{BC}\)
