vectơ

Question

Cho tam giác ABC . điểm M nằm trên cạnh Ac thỏa $MA = 3 MC $
a) phân tích theo hai vector BM theo hai vector BA và BC
b) cho 4 điểm A,B,C,D thỏa 2 vecto AB + 3 vecto $AC = 5$ vector AD chứng minh rằng ba điểm B,C,D thẳng hàng

score 0 · Answer 1

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