$AM=2AN$
$\to N$ là trung điểm $AM$
$d:\dfrac{x+1}{2}=\dfrac{y-2}{-1}=\dfrac{z+2}{3}$
$\to $ phương trình tham số: $d:\begin{cases}x=2t-1\\y=-t+2\\z=3t-2\end{cases}$
$M\in d\to M\left( \,\,2t-1\,\,;\,\,-t+2\,\,;\,\,3t-2\,\, \right)$
$A\left( \,\,1\,\,;\,\,1;\,\,-2\,\, \right)$
$N$ là trung điểm $AM$
$\to\begin{cases}x_N=\dfrac{x_A+x_M}{2}\\\\y_N=\dfrac{y_A+y_M}{2}\\\\z_N=\dfrac{z_A+z_M}{2}\end{cases}\,\,\,\to\,\,\,\,\,\begin{cases}x_N=t\\\\y_N=\dfrac{-t+3}{2}\\\\z_N=\dfrac{3t-4}{2}\end{cases}\,\,\,\to\,\,\,\,\,N\left(\,\,t\,\,;\,\,\dfrac{-t+3}{2}\,\,;\,\,\dfrac{3t-4}{2}\,\,\right)$
$N\in \left( P \right):\,\,\,x+2y-2z+2=0$
$\to \,\,\,t\,\,+\,\,2.\dfrac{-t+3}{2}\,\,-\,\,2.\dfrac{3t-4}{2}\,\,+\,\,2\,\,=0$
$\to \,\,\,t=3$
$\to N\left( \,\,3;\,\,0\,\,;\,\,\dfrac{5}{2}\,\, \right)$
$\to \overrightarrow{AN}=\left( \,\,2\,\,;\,\,-1\,\,;\,\,\dfrac{9}{2}\,\, \right)$ là VTCP của $\Delta $
$\to \overrightarrow{AN}=\left( \,\,8\,\,;\,\,-4\,\,;\,\,18\,\, \right)$ là VTCP của $\Delta $
