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PCAD所成的角的大小;

(3)    求二面角P—BD—A的大小.

 

【答案】

【解析】                   

         (1)          AD⊥面PAB···································· 4分

                 

(2) ADBCPCB(或其补角)为异面直线PCAD所成角

  

·············································· 8分

(3) 作PMABMMOBDO

      MOBD

 

PMAB

PMPAB

 

 

             

           为二面角P—BD—A的平面角························· 10分

  ················································· 12分

 

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