a) Trong \(\left( {ABD} \right)\), gọi \(E = MP \cap BD\)
\(\begin{array}{l}\left\{ \begin{array}{l}E \in BD \subset \left( {BCD} \right) \Rightarrow E \in \left( {BCD} \right)\\E \in MP \subset \left( {MNP} \right) \Rightarrow E \in \left( {MNP} \right)\end{array} \right.\\ \Rightarrow E \in \left( {BCD} \right) \cap \left( {MNP} \right)\\\left\{ \begin{array}{l}N \in CD \subset \left( {BCD} \right) \Rightarrow N \in \left( {BCD} \right)\\N \in \left( {MNP} \right)\end{array} \right.\\ \Rightarrow N \in \left( {BCD} \right) \cap \left( {MNP} \right)\\ \Rightarrow NE = \left( {BCD} \right) \cap \left( {MNP} \right)\end{array}\)
b) Trong mặt phẳng \((BCD)\) gọi \(Q\) là giao điểm của \(NE\) và \(BC\) ta có:
\(\left\{ \begin{array}{l}Q \in BC\\Q \in NE \subset \left( {MNP} \right) \Rightarrow Q \in \left( {MNP} \right)\end{array} \right.\\ \Rightarrow Q = BC \cap \left( {MNP} \right)\)
