Cho đường thẳng d: (x-2)/-1 = (y+1)/-1 = (z+1)/1 và mặt phẳng (P): 2x +y -2z =0

* Hướng dẫn giải

Đáp án B.

Gọi $A=d\cap \left(P\right)\Rightarrow A\left(-t+2;-t-1;t-1\right)$

$$\begin{gathered} \Rightarrow 2\left(-t+2\right)+\left(-t-1\right)-2\left(t-1\right)=0 \\ \iff -5t+5=0\iff t=1\Rightarrow A\left(1;-2;0\right). \end{gathered}$$

Ta có:

$$\begin{gathered} \left\{\begin{array}{l}\overrightarrow{u_d}=\left(-1;-1;1\right)\\ \overrightarrow{u_p}=\left(2;1;-2\right)\end{array}\right. \\ \Rightarrow \left[\overrightarrow{u_d};\overrightarrow{u_p}\right]=\left(1;0;1\right) \\ \Rightarrow \Delta :\left\{\begin{array}{l}x=1-t\\ y=-2\\ z=-t\end{array}\right.\left(t\in \mathbb{Z}\right). \end{gathered}$$