Question

Tìm m để A(1; 2; 1), B(2; m; 0)và C(4; -2; 5)và D(6; 6; 6)đồng phẳng.
 

Answer 1

\(\overrightarrow{AC}=\left(3; -4; 4\right), \overrightarrow{AD}=\left(5; 4; 5\right), \overrightarrow{AB}=\left(1; m-2; -1\right), \left[\overrightarrow{AC},\overrightarrow{AD}\right]=\left(-36; 5; 32\right) \)
\(A,{\rm  }B,{\rm  }C,{\rm  }D \) đồng phẳng \(\Leftrightarrow \overrightarrow{AC}, \overrightarrow{AD}, \overrightarrow{AB}\) đồng phẳng \(\Leftrightarrow \left[\overrightarrow{AC},\overrightarrow{AD}\right].\overrightarrow{AB}=0 \)
\(\Leftrightarrow -36+5(m-2)-32=0\Leftrightarrow m=\frac{78}{5} .  \)