Lời giải:
Từ điều kiện đề suy ra:
\(-2\overrightarrow{EC}=\overrightarrow{EB}\Rightarrow -3\overrightarrow{EC}=\overrightarrow{EB}-\overrightarrow{EC}=\overrightarrow{CB}\)
\(\Rightarrow \overrightarrow{EC}=\frac{-1}{3}\overrightarrow{CB}=\frac{1}{3}\overrightarrow{BC}\)
\(3\overrightarrow{CF}=\overrightarrow{DF}\Rightarrow 2\overrightarrow{CF}=\overrightarrow{DF}-\overrightarrow{CF}=\overrightarrow{DC}\)
\(\Rightarrow \overrightarrow{CF}=\frac{1}{2}\overrightarrow{DC}\)
Thực hiện biến đổi:
\(\overrightarrow{EF}=\overrightarrow{EC}+\overrightarrow{CF}=\frac{1}{3}\overrightarrow{BC}+\frac{1}{2}\overrightarrow{DC}(*)\)
\(\overrightarrow{AF}=\overrightarrow{AD}+\overrightarrow{DF}=\overrightarrow{BC}+\overrightarrow{DC}+\overrightarrow{CF}\)
\(=\overrightarrow{BC}+\overrightarrow{DC}+\frac{1}{2}\overrightarrow{DC}=3(\frac{1}{3}\overrightarrow{BC}+\frac{1}{2}\overrightarrow{DC})=3\overrightarrow{EF}\)
\(\Rightarrow A,E,F\) thẳng hàng.
