题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-98489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-19609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(1)问BC边上是否存在点Q,使得PQ
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(2)若边上有且只有一个点Q,使得PQ
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-37586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-23017.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-13635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(ii)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-50810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-80635.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-28769.png)
则Q
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-98213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-70296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-29004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-26308.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-27363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001039-37165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001040-49629.png)
若方程①有解,必为正数解,且小于
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-98489.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001040-78320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001040-77533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-13635.png)
(i)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-13635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(ii)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-50810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
(2)要使BC边上有且只有一个点Q,使PQ
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001037-58746.png)
这时,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001040-54286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001040-41761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001041-54830.png)
又平面APD的法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001041-11254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001041-12498.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001041-92888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001042-75140.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001042-17209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001042-35285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001042-25411.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001042-45937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001043-30997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001043-56539.png)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001043-44426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001038-80635.png)
核心考点
试题【如图,已知矩形ABCD中,AB=1,BC=,PA平面ABCD,且PA=1。(1)问BC边上是否存在点Q,使得PQQD?并说明理由;(2)若边上有且只有一个点Q,】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001026-95401.png)
A.![]() | B.![]() | C.![]() | D.![]() |
A.![]() | B.![]() |
C.![]() | D.![]() |
(1)求证:平面AOC⊥平面BCD;
(2)若三棱锥A—BCD的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001005-28876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001006-33957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021001006-62549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000956-44091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000956-55862.png)
A.相交 | B.平行 | C.异面而且垂直 | D.异面但不垂直 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000957-29486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000948-40418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000948-31535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000949-61587.png)
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