a) \underset{BM}{\rightarrow}=\underset{BA}{\rightarrow}+\underset{AM}{\rightarrow}=\underset{BA}{\rightarrow}+\underset{AC}{\rightarrow}+\underset{CM}{\rightarrow}= -2\underset{BA}{\rightarrow}-\frac{3}{4}\underset{BC}{\rightarrow}+\underset{BC}{\rightarrow}+\frac{3}{4}\underset{BA}{\rightarrow}=\frac{-5}{4}\underset{BA}{\rightarrow}+\frac{1}{4}\underset{BC}{\rightarrow}
b)2\underset{AB}{\rightarrow}+3\underset{AC}{\rightarrow}=5\underset{AD}{\rightarrow}
\Leftrightarrow 2\underset{AB}{\rightarrow}+3\underset{AC}{\rightarrow}-5\underset{AD}{\rightarrow}=\underset{0}{\rightarrow}
\Leftrightarrow(2\underset{AB}{\rightarrow}-2\underset{AD}{\rightarrow})+(3\underset{AC}{\rightarrow}-3\underset{AD}{\rightarrow})=\underset{0}{\rightarrow}
\Leftrightarrow2\underset{DB}{\rightarrow}=-3\underset{DC}{\rightarrow}
\Rightarrow ba điểm B,C,D thẳng hàng