题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-49755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-89960.png)
(1)求证:BE//平面D1AC;
(2)求证:AF⊥BE;
(3)求异面直线AF与BD所成角的余弦值。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-86992.png)
解析
试题分析:(1)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-54416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-79868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-21729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-70171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-98643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-73808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-70171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-73808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-77142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-64291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114311-19497.png)
试题解析:
(1)(方法一)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-54416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-79868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-21729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-70171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114311-71167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114311-55258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114312-10214.png)
所以四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-98643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-73808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-70171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114312-58511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-77142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114312-59505.png)
面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-77142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-73808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-77142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114312-23155.png)
(方法二)以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114313-68663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114313-57394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114313-61018.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114313-15171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114314-34725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114314-37888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114314-75132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114314-80677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114315-44208.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114315-99927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-73808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114310-77142.png)
(2)由(1)的方法二可知
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114315-57639.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114315-96872.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114316-19175.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114316-97394.png)
(3)由(1)、(2)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114316-86833.png)
的角为q,则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114317-96167.png)
故异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114317-51811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114317-66701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114309-86992.png)
核心考点
试题【如图,在长方体AC1中,AB=BC=2,,点E、F分别是面A1C1、面BC1的中心.(1)求证:BE//平面D1AC;(2)求证:AF⊥BE;(3)求异面直线A】;主要考察你对空间向量的基本概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114247-31389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114247-31389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114247-31389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114247-41890.jpg)
(1)求证:BM∥平面PAD;
(2)在侧面PAD内找一点N,使MN
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114247-31389.png)
(3)求直线PC与平面PBD所成角的正弦。
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114235-52492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114235-29835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114235-41401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114236-78443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114236-26815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114236-35340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114236-80471.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114237-24157.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114237-27845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114222-40387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114222-51977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114222-78424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114222-28541.jpg)
(1)当点M为EC中点时,求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114223-27322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114223-26405.png)
(2)若平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114223-61143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114223-99540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114223-12153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114210-26300.jpg)
(1)求异面直线A1B与C1D所成角的余弦值;
(2)求平面ADC1与平面ABA1所成二面角的正弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105114205-98030.png)
(1)求证:BE∥平面PAD;
(2)若BE⊥平面PCD,求平面EBD与平面BDC夹角的余弦值.
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