如圖1,在Rt△ABC中,∠C=90°,BC=3,AC=6,D,E分別是AC,AB上的點,且DE∥BC,DE=2,將△ADE沿DE折起到△A
1DE的位置,使A
1C⊥CD,如圖2.
(I)求證:A
1C⊥平面BCDE;
(II)若M是A
1D的中點,求CM與平面A
1BE所成角的大小;
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(I)先證
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(II)
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試題分析:(1)
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,
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平面
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,
又
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平面
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,
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又
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,
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平面
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。
(2)如圖建系
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,則
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,
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,
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,
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∴
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,
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設(shè)平面
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法向量為
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則
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∴
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∴
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∴
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又∵
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∴
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∴
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,
∴
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與平面
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所成角的大小
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.
點評:本題考查線面垂直,考查線面角,考查面面垂直,既有傳統(tǒng)方法,又有向量知識的運用,要加以體會.
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
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
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
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
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
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,
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
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
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
;
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的大�。�
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
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
⊥平面

,

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
.
(1)求證:對任意的
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
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已知空間三點
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
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
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