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Câu 1:
\(\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)
\(=\dfrac{1}{3}\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{AC}\)
\(\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\dfrac{2}{3}\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)
\(=\dfrac{1}{3}\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{AC}\)
Hình bạn tự vẽ :
AM=AB+BM
=AB+2/3BC
=AB +2/3(BA+AC)
=AB-2/3AB+2/3C
= 1/3 AB + 2/3AC
\(\overrightarrow{AM}=\overrightarrow{AB}+\overrightarrow{BM}\)
\(=\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BC}\)
\(=\overrightarrow{AC}+\overrightarrow{CB}+\dfrac{3}{4}\overrightarrow{BC}\)
\(=\overrightarrow{AC}-\dfrac{1}{4}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\overrightarrow{BC}-\dfrac{1}{4}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BC}\)
\(=\overrightarrow{AB}+\dfrac{3}{4}\left(\overrightarrow{BA}+\overrightarrow{AC}\right)\)
\(=\dfrac{1}{4}\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{AC}\)
vecto AN+vecto BP+vecto CM
=vecto AB+vecto BN+vecto BC+vecto CP+vecto CA+vecto AM
=vecto AB+1/3vecto BC+vecto BC+1/3vecto CA+vecto CA+1/3vecto AB
=4/3 vecto AB+4/3vecto BC+4/3vecto CA
=vecto 0
Vì MB = 2MC (M thuộc đoạn BC)
\(\Rightarrow\overrightarrow{MB}=-2\overrightarrow{MC}\\ \Leftrightarrow\overrightarrow{MA}+\overrightarrow{AB}=-2\overrightarrow{MA}-2\overrightarrow{AC}\\ \Leftrightarrow3\overrightarrow{AM}=\overrightarrow{AB}+2\overrightarrow{AC}\\ \Leftrightarrow\overrightarrow{AM}=\dfrac{1}{3}\overrightarrow{AB}+\dfrac{2}{3}\overrightarrow{AC}\)