gaokao 2024 Q17

gaokao · China · beijing Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines
Given a quadrangular pyramid $P - ABCD$, where $AD \parallel BC$, $AB = BC = 1$, $AD = 3$, $DE = PE = 2$, $E$ is a point on $AD$, and $PE \perp AD$.
(1) If $F$ is the midpoint of $PE$, prove that $BF \parallel$ plane $PCD$.
(2) If $AB \perp$ plane $PED$, find the cosine of the dihedral angle between plane $PAB$ and plane $PCD$. 
Given a quadrangular pyramid $P - ABCD$, where $AD \parallel BC$, $AB = BC = 1$, $AD = 3$, $DE = PE = 2$, $E$ is a point on $AD$, and $PE \perp AD$.\\
(1) If $F$ is the midpoint of $PE$, prove that $BF \parallel$ plane $PCD$.\\
(2) If $AB \perp$ plane $PED$, find the cosine of the dihedral angle between plane $PAB$ and plane $PCD$.
Paper Questions
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