题目内容
1. (本小题满分12分)
如图,在四棱锥P—ABCD中,底面ABCD是矩形,已知AB = 3,AD = 2,PA = 2,
,
.
(1) 证明:AD⊥平面PAB;
(2) 求异面直线PC与AD所成的角的大小;
(3) 求二面角P—BD—A的大小.
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【答案】
(1)略(2)
(3)略
【解析】
(1)
AD⊥面PAB···································· 4分
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(2) AD∥BC
∠PCB(或其补角)为异面直线PC与AD所成角
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·············································· 8分
(3) 作PM⊥AB于M,MO⊥BD于O
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为二面角P—BD—A的平面角························· 10分
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12分
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