Ta có: [tex]\overrightarrow{IB}+3\overrightarrow{IC}=\overrightarrow{0}\Rightarrow \Rightarrow \overrightarrow{IB}=-\frac{3}{4}\overrightarrow{BC}\Rightarrow \overrightarrow{MI}=\overrightarrow{MB}+\overrightarrow{BI}=\frac{1}{2}\overrightarrow{AB}+\frac{3}{4}\overrightarrow{BC}[/tex]
[tex]\overrightarrow{KC}=m\overrightarrow{KA}\Rightarrow m\overrightarrow{KA}=\overrightarrow{KA}+\overrightarrow{AC}\Rightarrow \overrightarrow{KA}=\frac{1}{m-1}\overrightarrow{AC}\Rightarrow \overrightarrow{MK}=\overrightarrow{MA}+\overrightarrow{AK}=-\frac{1}{2}\overrightarrow{AB}+\frac{1}{1-m}(\overrightarrow{AB}+\overrightarrow{BC})=(\frac{1}{1-m}-\frac{1}{2})\overrightarrow{AB}+\frac{1}{1-m}\overrightarrow{BC}[/tex]
Để I,K,M thẳng hàng thì [tex]\overrightarrow{MI}=k\overrightarrow{MK}[/tex] [tex]\Leftrightarrow \frac{1}{1-m}:(\frac{1}{1-m}-\frac{1}{2})=\frac{3}{4}:\frac{1}{2}=\frac{3}{2}\Leftrightarrow \frac{1}{1-m}=\frac{3}{2}\Leftrightarrow m=\frac{1}{3}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
