gaokao 2020 Q19

gaokao · China · national-III-arts 12 marks Vectors: Lines & Planes Prove Perpendicularity/Orthogonality of Line and Plane
As shown in the figure, in the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$, points $E , F$ are on edges $D D _ { 1 } , B B _ { 1 }$ respectively, with $2 D E = E D _ { 1 } , B F = 2 F B _ { 1 }$. Prove:
(1) When $A B = B C$, $E F \perp A C$;
(2) Point $C _ { 1 }$ lies in plane $A E F$. 
As shown in the figure, in the rectangular prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$, points $E , F$ are on edges $D D _ { 1 } , B B _ { 1 }$ respectively, with $2 D E = E D _ { 1 } , B F = 2 F B _ { 1 }$. Prove:\\
(1) When $A B = B C$, $E F \perp A C$;\\
(2) Point $C _ { 1 }$ lies in plane $A E F$.
Paper Questions
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