题干

如图,四棱锥P﹣ABCD中,底面ABCD为矩形,PA⊥平面ABCD,E为PD的中点.
(Ⅰ)证明:PB∥平面AEC;
(Ⅱ)设二面角D﹣AE﹣C为60°,AP=1,AD= 3 ,求三棱锥E﹣ACD的体积.
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答案(点此获取答案解析)

(Ⅰ)证明:连接BD交AC于O点,连接EO,

∵O为BD中点,E为PD中点,

∴EO∥PB,

EO⊂平面AEC,PB⊄平面AEC,所以PB∥平面AEC;

(Ⅱ)解:延长AE至M连结DM,使得AM⊥DM,

∵四棱锥P﹣ABCD中,底面ABCD为矩形,PA⊥平面ABCD,

∴CD⊥平面AMD,

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    The booking notes of the play “The Age of Innocence”:

    Price: $10

    DISCOUNTS;

    Saver: $2 off any seat booked any time in advance for performances from Monday to Thursday. Savers are available for children under 16, over 60s and full-time students.

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    Please note: We are unable to exchange tickets or refund (退款) money unless a performance is cancel led due to unforeseen circumstances.

BOOKING:

    There are four easy ways to book seats for performance:

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