Đáp án:

- Mp \( P: ax + by + cz + d = 0 \)  
  Mp \( P \) qua \( M(1,0,0) \)   \( \Rightarrow a + d = 0 \Rightarrow d = -a. \)  
  Mp \( P \) qua \( N(0,0,-1) \)   \( \Rightarrow -c + d = 0 \Rightarrow c = d = -a. \)  
\( \Rightarrow \text{Mp } P: ax + by - az - a = 0 \Rightarrow \vec{n}_P = (a, b, -a). \)  

- \( \vec{n}_Q = (1, -1, 0). \)  
  Góc \(((P), (Q)) = 45^\circ \Leftrightarrow  \cos (45^\circ) = | \cos{(\vec{n_P, n_Q})}|\)

\( \Leftrightarrow \frac{|a - b|}{\sqrt{a^2 + b^2 + a^2} \sqrt{2}} = \frac{\sqrt{2}}{2} \Leftrightarrow |a - b| = \sqrt{2a^2 + b^2}. \)  

  \( \Rightarrow a^2 + b^2 - 2ab = 2a^2 + b^2 \Leftrightarrow a^2 + 2ab = 0 . \)  

- \( \left[ \begin{split} &a=0 (\text{ Chọn b = 1}): \quad &y = 0 \\ &a=-2b (\text{ Chọn b = -1}): \quad &2x - y - 2z - 2 = 0\end{split} \right. \Rightarrow \boxed{A} \)