Giải chi tiết:
+) Cho \(N \in d \Rightarrow N\left( { - 2 + 2t;1 + t;1 - t} \right)\).
+) Do A là trung điểm MN \( \Rightarrow A = \dfrac{{M + N}}{2} \Rightarrow M = 2A - N \Rightarrow M\left( {4 - 2t;5 - t;3 + t} \right)\)
+) Do \(M \in \left( P \right) \Rightarrow 2\left( {4 - 2t} \right) - \left( {5 - t} \right) + 3 + t - 10 = 0\) \( \Leftrightarrow t = - 2\)
\(\begin{array}{l} \Rightarrow \left\{ \begin{array}{l}M\left( {8;7;1} \right)\N\left( { - 6; - 1;3} \right)\end{array} \right.\ \Rightarrow \Delta \,\,\left\{ \begin{array}{l}qua\,\,N\left( { - 6; - 1;3} \right)\\overrightarrow u = \overrightarrow {NM} = \left( {14;8; - 2} \right) = 2\left( {7;4; - 1} \right)\end{array} \right.\end{array}\)
\( \Rightarrow \Delta :\,\,\dfrac{{x + 6}}{7} = \dfrac{{y + 1}}{4} = \dfrac{{z - 3}}{{ - 1}}\).