a: \(\overrightarrow{MB}-3\cdot\overrightarrow{MC}=\overrightarrow{0}\)
=>\(\overrightarrow{MB}=3\cdot\overrightarrow{MC}\)
=>MB=3MC và C nằm giữa M và B
MC+CB=MB
=>BC=MB-MC=3MC-MC=2MC
\(\overrightarrow{NB}+2\cdot\overrightarrow{NA}=\overrightarrow{0}\)
=>\(\overrightarrow{NB}=-2\cdot\overrightarrow{NA}\)
=>N nằm giữa B và A sao cho NB=2NA
AN+NB=AB
=>AB=AN+2AN=3AN
=>\(AN=\frac13AB;BN=\frac23BA\)
\(\overrightarrow{AM}=\overrightarrow{AC}+\overrightarrow{CM}\)
\(=\overrightarrow{AC}+2\cdot\overrightarrow{BC}=\overrightarrow{AC}+2\left(\overrightarrow{BA}+\overrightarrow{AC}\right)=-2\cdot\overrightarrow{AB}+3\cdot\overrightarrow{AC}\)
\(\overrightarrow{MC}=2\cdot\overrightarrow{CB}=2\left(\overrightarrow{CA}+\overrightarrow{AB}\right)=2\cdot\overrightarrow{AB}-2\cdot\overrightarrow{AC}\)
