题干

在四棱锥P﹣ABCD中,△PAB为正三角形,四边形ABCD为矩形,平面PAB⊥平面ABCD,AB=2AD,M,N分别为PB,PC中点.

(Ⅰ)求证:MN∥平面PAD;

(Ⅱ)求二面角B﹣AM﹣C的大小;

(Ⅲ)在BC上是否存在点E,使得EN⊥平面AMN?若存在,求

B
E
B
C
的值;若不存在,请说明理由.

上一题 下一题 0.0难度 选择题 更新时间:2012-12-12 09:37:36

答案(点此获取答案解析)

证明:(Ⅰ)∵M,N分别是PB,PC中点

∴MN是△ABC的中位线

∴MN∥BC∥AD

又∵AD⊂平面PAD,MN⊄平面PAD

所以MN∥平面PAD.

解:(Ⅱ)过点P作PO垂直于AB,交AB于点O,

因为平面PAB⊥平面ABCD,所以PO⊥平面ABCD,

如图建立空间直角坐标系,

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