题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032129-80985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032129-63384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032129-94584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032129-32970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-75366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-18696.png)
(Ⅰ)证明:平面ADB ⊥平面BDC;
(Ⅱ)设E为BC的中点,求AE与DB夹角的余弦值。
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-71005.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-31840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-92844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-67687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032131-72334.png)
解析
(2)作辅助线,取DC中点F,连接EF,则EF∥BD,可得∠AEF为异面直线AE与BD所成的角,再根据余弦定理和向量公式进行求解;
解(Ⅰ)∵折起前AD是BC边上的高,
∴ 当Δ ABD折起后,AD⊥DC,AD⊥DB,又DB
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032131-75507.png)
∴AD⊥平面BDC,∵AD 平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032131-19520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032131-28844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032132-67384.png)
(Ⅱ)由∠ BDC=
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032132-69862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032132-18743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032132-92541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032133-64444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032133-87433.png)
易得D(0,0,0),B(1,0,0),C(0,3,0),A(0,0,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032133-64461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-34585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-85067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-33731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-48856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-67687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-33731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-67687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-31840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-92844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032130-67687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032134-47728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032131-72334.png)
核心考点
试题【 (本小题满分12分)如图,在中,是上的高,沿把折起,使 。(Ⅰ)证明:平面ADB ⊥平面BDC;(Ⅱ)设E为BC的中点,求AE与DB夹角的余弦值。】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
(1)求证:PC⊥BC;
(2)求点A到平面PBC的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032124-82821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032110-62830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032111-97345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032112-30976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032111-97345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032112-48711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032112-25382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032113-12498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032113-64664.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032113-10442.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032114-49812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032114-69144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032114-76535.png)
求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032114-32363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032058-22797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032058-18951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032059-66365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032059-18748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032059-37609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032059-66954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032059-81851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032100-37893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032100-98154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032100-89951.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032100-63875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032101-72633.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032100-63875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032101-48282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032101-75330.png)
如图,已知正方体
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032044-24716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032044-58573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032044-96235.png)
求证:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032044-55971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032045-94510.png)
(2 )
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032045-39793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032045-94510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032045-53116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032035-46490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032035-35554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032035-27667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-84423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-95950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-28658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-10588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-73103.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-10284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032037-41200.png)
(Ⅱ)在棱
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032036-84423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032037-18099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032037-35981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032037-74478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032037-58331.png)
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