题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-97579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-71784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-19563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-31330.jpg)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-73713.png)
(Ⅱ)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-19563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-10568.png)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-15329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-90738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-76955.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-28939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-91623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-80157.png)
解析
试题分析:(Ⅰ)建立空间直角坐标系,利用向量数量积为零证明即可;(Ⅱ)求出平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-10568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-20084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-35143.png)
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-29177.jpg)
以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-17289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-14000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025124-55885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025124-79222.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025124-35544.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025124-98736.png)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-19563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025125-88888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025125-11239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025125-85079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025125-97919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-10568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-35143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025126-43527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025126-61538.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025126-88117.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025126-38428.png)
所以点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025120-19563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-10568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025127-38075.png)
(3)设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-20084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025123-35143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025127-49079.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025127-36008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025127-99860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025128-58643.png)
依题意
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025128-57338.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025128-73574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025128-59212.png)
.∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025128-62667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025122-91623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025121-76955.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025108-93164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025108-33340.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-10043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-37669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-73108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-49322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-73108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-65082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025046-96594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-14407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-75434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-19544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-62687.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-12722.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-58680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025047-37736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025034-51120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025034-86680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025035-70757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025035-47881.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025035-46518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025035-92390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025036-60065.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025036-45630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025036-40159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025036-66684.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025036-60065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025037-10683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025037-67878.png)
④若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025037-20850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025037-66222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025038-58860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025037-67878.png)
其中真命题的是( )
A.①和② | B.②和③ | C.③和④ | D.②和④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-26755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-95263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-58671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-26755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-50910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025019-57192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025019-79965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025019-86250.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025019-36195.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025020-43126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025020-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025018-50910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025020-80875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025020-47548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025006-27349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025007-61631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025007-22442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025007-56623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025007-81803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025008-96020.jpg)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025008-19962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025008-89596.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025008-50064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106025008-95169.png)
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