M là trung điểm BC.
CI−→=CA−→−+AI−→=−AC−→−+13AM−→−=−AC−→−+16(AB−→−+AC−→−)=16AB−→−−56AC−→−
CK−→−=CA−→−+AK−→−=−AC−→−+15AB−→−=65CI−→
Suy ra C, I, K thẳng hàng.
M là trung điểm BC
\(\overrightarrow{CI}=\overrightarrow{CA}+\overrightarrow{AI}=\overrightarrow{-AC}+\frac{1}{3}\overrightarrow{AM}=\overrightarrow{-AC}+\frac{1}{6}\left(\overrightarrow{AB}+\overrightarrow{AC}\right)=\frac{1}{6}\overrightarrow{AB}-\frac{5}{6}\overrightarrow{AC}\)
\(\overrightarrow{CK}=\overrightarrow{CA}+\overrightarrow{AK}=\overrightarrow{-AC}+\frac{1}{5}\overrightarrow{AB}=\frac{6}{5}\overrightarrow{CI}\)
\(\Rightarrow\) C, I, K thẳng hàng