Trong không gian Oxyz cho đường thẳng $\Delta...

Ta có: \)">\Delta :\dfrac{x}{1}=\dfrac{y+1}{2}=\dfrac{z-1}{1}\Rightarrow \Delta :\left\{ \begin{aligned}
& x=t \\
& y=-1+2t \\
& z=1+t \\
\end{aligned} \right. M=\Delta \cap P\Rightarrow M\in \Delta \Rightarrow M\left( t;2t-1;t+1 \right),M\in P\Rightarrow t-2\left( 2t-1 \right)-(t+1)+3=0\Leftrightarrow 4-4t=0\Leftrightarrow t=1\Rightarrow M\left( 1;1;2 \right)\overrightarrow{n}=\left( 1;-2;-1 \right)\overrightarrow{u}=\left( 1;2;1 \right)\Rightarrow \dfrac{1}{2}\left[ \overrightarrow{n},\overrightarrow{u} \right]=\left( 0;-1;2 \right)M\left( 1;1;2 \right)\in d\Rightarrow d:\left\{ \begin{aligned}
& x=1 \\
& y=1-t \\
& z=2+2t \\
\end{aligned} \right.$