Câu hỏi 10

Gọi \(H \in SD\) sao cho \(HD = {1 \over 2}SH\)

Ta có: \({{SM} \over {SE}} = {{SH} \over {SD}} = {2 \over 3} \Rightarrow MH//AD//NP \Rightarrow M,H,P,N\) đồng phẳng.

Ta có:

\(\eqalign{  & {{AN} \over {AC}} = {{DP} \over {DC}} = {1 \over 3} \Rightarrow NP//AD;\,\,{{DH} \over {DS}} = {{DP} \over {DC}} = {1 \over 3} \Rightarrow HP//SC  \cr   & \left\{ \matrix{  NP//AD//BC \hfill \cr   HP//SC \hfill \cr}  \right. \Rightarrow \left( {MHPN} \right)//\left( {SBC} \right) \Rightarrow \left( {MNP} \right)//\left( {SBC} \right)  \cr   & MN \subset \left( {MNP} \right) \Rightarrow MN//\left( {SBC} \right) \cr} \)

Chọn A.