Trong không gian $Oxyz$, cho mặt phẳng $(P): x+2y-z-1=0$, điểm...

Điểm thuộc đoạn thẳng AN
Điểm
$\Leftrightarrow \left\{ \begin{aligned}
& 2-2t=-3{{x}_{n}}-3+6t \\
& -1-t=-3{{y}_{n}}+3+3t \\
& 2-t=-3{{z}_{n}}+3t \\
\end{aligned} \right.$$\Rightarrow N\left( \dfrac{8t-5}{3};\dfrac{4t+4}{3};\dfrac{4t-2}{3} \right).N\in (P):x+2y-z-1=0\Rightarrow \dfrac{8t-5}{3}+2.\dfrac{4t+4}{3}-\dfrac{4t-2}{3}-1=0\Rightarrow t=-\dfrac{1}{6}.\Rightarrow M\left( \dfrac{-4}{3};\dfrac{5}{6};\dfrac{-1}{6} \right);N\left( \dfrac{-19}{9};\dfrac{10}{9};\dfrac{-8}{9} \right)\Rightarrow \overrightarrow{NM}\left( \dfrac{7}{9};\dfrac{-10}{36};\dfrac{26}{36} \right)=\left( 14;-5;13 \right).\Rightarrow \Delta :\dfrac{x-1}{14}=\dfrac{y}{-5}=\dfrac{z-2}{13}.$