如图，在长方体ABCD﹣A1B1C1D1中，AD=AA1=1，AB=2，点E在棱AB上．（Ⅰ）求异面直线D1E与A1D所成的角；（Ⅱ）若二面角D1﹣EC﹣D的大小为45°，求点B到平面D1EC的距

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如图，在长方体ABCD﹣A₁B₁C₁D₁中，AD=AA₁=1，AB=2，点E在棱AB上．

（Ⅰ）求异面直线D₁E与A₁D所成的角；

（Ⅱ）若二面角D₁﹣EC﹣D的大小为45°，求点B到平面D₁EC的距离．

上一题下一题 0.0难度选择题更新时间:2019-02-07 08:19:47

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解：解法一：（Ⅰ）连结AD₁．由AA₁D₁D是正方形知AD₁⊥A₁D．

∵AB⊥平面AA₁D₁D，

∴AD₁是D₁E在平面AA₁D₁D内的射影．

根据三垂线定理得AD₁⊥D₁E，

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