Đáp án:

\(mp R\):

\( (x - 2y + z - 1) + m(2x + y - 3z + 1) = 0 \)  

\( (1 + 2m)x + (m - 2)y + (1 - 3m)z - 1 + m = 0 \)

\( \overrightarrow{AB} = (1, 2, 1) // \text{mp P} \)

\( \Rightarrow \overrightarrow{AB} = (1, 2, 1) \perp \overrightarrow{n_P} = (1 + 2m, m - 2, 1 - 3m) \)

\( \Rightarrow 1 + 2m + 2m - 4 + 1 - 3m = 0 \Leftrightarrow m = 2 \)

\(mp (R):  5x - 5z + 1 = 0 \Rightarrow \boxed{D}\)