gaokao 2015 Q17

gaokao · China · fujian-science Vectors 3D & Lines Dihedral Angle Computation
17. In the geometric solid ABCDE shown in the figure, quadrilateral ABCD is a rectangle, $AB \perp$ plane $BEC$, $BE \perp EC$, $AB = BE = EC = 2$, and $G$ and $F$ are the midpoints of segments $BE$ and $DC$ respectively.
(1) Prove that $GF \parallel$ plane $ADE$.
(2) Find the cosine of the acute dihedral angle between plane $AEF$ and plane $BEC$. 
17. In the geometric solid ABCDE shown in the figure, quadrilateral ABCD is a rectangle, $AB \perp$ plane $BEC$, $BE \perp EC$, $AB = BE = EC = 2$, and $G$ and $F$ are the midpoints of segments $BE$ and $DC$ respectively.\\
(1) Prove that $GF \parallel$ plane $ADE$.\\
(2) Find the cosine of the acute dihedral angle between plane $AEF$ and plane $BEC$.
Paper Questions
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