a) $\overrightarrow{A P}+\frac{1}{2} \overrightarrow{B C}=\frac{1}{2}\overrightarrow{AB}+\frac{1}{2} \overrightarrow{B C}=\frac{1}{2} \overrightarrow{AC}=\overrightarrow{A N}$ (đpcm).
b) $\overrightarrow{B C}+2 \overrightarrow{M P}=2\overrightarrow{BM}+2 \overrightarrow{M P}=2 \overrightarrow{B P}=\overrightarrow{B A}$(đpcm).