如圖,平面
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平面
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是正方形,
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是矩形,且
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,
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是
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的中點.
(1)求
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與平面
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所成角
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的正弦值;
(2)求二面角
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的余弦值.
(1)
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(2)
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如圖所示,建立空間直角坐標系.
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則
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.
(1) 由題意可得
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,
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.
設(shè)平面
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的法向量
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,
由
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.
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.
(2) 因
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是平面
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的法向量,又
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平面
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,
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是平面
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的法向量.
得
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.
故二面角
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的余弦值為
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.
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如圖,四棱錐
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中,

,底面
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為直角梯形,
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,點
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在棱
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上,且
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.
(1)求異面直線
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與
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所成的角;
(2)求證:
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平面
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;
(3)求二面角
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的余弦值.

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已知直三棱柱
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中,△
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為等腰直角三角形,∠
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=90°,且
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=
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,
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、
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、
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分別為
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、
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、
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的中點.

(1)求證:
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∥平面
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;
(2)求證:
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⊥平面
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;
(3)求二面角

的余弦值
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已知空間四面體
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的每條邊都等于1,點
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分別是
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的中點,則
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等于 �。� )

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已知正方體

的棱長為2,
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分別是
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上的動點,且

,確定
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的位置,使
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.
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以下說法中,正確的個數(shù)是( )
①平面
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內(nèi)有一條直線和平面
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平行,那么這兩個平面平行
②平面

內(nèi)有兩條直線和平面

平行,那么這兩個平面平行
③平面
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內(nèi)有無數(shù)條直線和平面

平行,那么這兩個平面平行
④平面
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內(nèi)任意一條直線和平面
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都無公共點,那么這兩個平面平行
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