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Câu hỏi: Trong không gian Oxzyz, cho mặt phẳng $\left( P \right):2x-y+2z-3=0$ và đường thẳng $\left( \Delta \right):\dfrac{x-1}{2}=\dfrac{y+1}{2}=\dfrac{z-1}{-1}$. Khoảng cách giữa $\left( \Delta \right)$ và $\left( P \right)$ là
A. $\dfrac{2}{3}$.
B. $\dfrac{8}{3}$.
C. $\dfrac{2}{9}$.
D. 1.
A. $\dfrac{2}{3}$.
B. $\dfrac{8}{3}$.
C. $\dfrac{2}{9}$.
D. 1.
Ta có $\left\{ \begin{aligned}
& M\left( 1;-1;1 \right)\in \Delta \\
& M\notin \left( P \right) \\
& 2.2+\left( -1 \right).2+2.\left( -1 \right)=0 \\
\end{aligned} \right.$
$\Rightarrow \Delta //\left( P \right)\Rightarrow d\left( \Delta ;\left( P \right) \right)=d\left( M;\left( P \right) \right)=\dfrac{\left| 2.1-\left( -1 \right).2+2.1-3 \right|}{\sqrt{{{2}^{2}}+{{\left( -1 \right)}^{2}}+{{2}^{2}}}}=\dfrac{2}{3}$.
& M\left( 1;-1;1 \right)\in \Delta \\
& M\notin \left( P \right) \\
& 2.2+\left( -1 \right).2+2.\left( -1 \right)=0 \\
\end{aligned} \right.$
$\Rightarrow \Delta //\left( P \right)\Rightarrow d\left( \Delta ;\left( P \right) \right)=d\left( M;\left( P \right) \right)=\dfrac{\left| 2.1-\left( -1 \right).2+2.1-3 \right|}{\sqrt{{{2}^{2}}+{{\left( -1 \right)}^{2}}+{{2}^{2}}}}=\dfrac{2}{3}$.
Đáp án A.