a)Ta có : $2\overrightarrow{IA}+3\overrightarrow{IB}=\overrightarrow{O}\Leftrightarrow 2\overrightarrow{IA}=3\overrightarrow{BI}\Leftrightarrow \frac{\overrightarrow{IA}}{\overrightarrow{BI}}=\frac{3}{2}\Leftrightarrow \overrightarrow{AI}=\frac{2}{5}\overrightarrow{AB}$Vậy k=2/5
b)Gọi C là điểm đối xứng vs A wa I ta có :
$\overrightarrow{MI}=\frac{1}{2}\overrightarrow{MA}+\frac{1}{2}\overrightarrow{MC}=\frac{1}{2}\overrightarrow{MA}+\frac{1}{2}(\overrightarrow{MB}+\overrightarrow{BC})=\frac{1}{2}\overrightarrow{MA}+\frac{1}{2}\overrightarrow{MB}+\frac{1}{10}(\overrightarrow{MA}-\overrightarrow{MB})=\frac{3}{5}\overrightarrow{MA}+\frac{2}{5}\overrightarrow{MB}$(đpcm)
Vậy ........
~~~~~~$Amen$~~~~~~