题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-27879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-72409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-23162.png)
A.![]() | B.![]() | C.![]() | D.![]() |
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111554-22196.jpg)
以A为原点建立空间直角坐标系,如图.
设棱长为1,则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111554-78048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111554-34580.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111554-81650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111555-42671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111555-59344.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-23162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111555-70929.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111555-62893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111556-35187.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111555-70929.png)
设平面ABCD的一个法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111556-40706.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111556-86289.png)
即平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-23162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111553-25500.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111541-22680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111542-41270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111542-10787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111542-28028.png)
A.![]() | B.![]() | C.![]() | D.![]() |
①若向量
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111528-54855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111528-21683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-58124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111528-54855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-23256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-65765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-23256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111528-54855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-92240.png)
②若等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-12947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111530-42380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111530-56157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111530-56157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111530-28429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111530-67491.png)
③常数列既是等差数列,又是等比数列;
④若向量
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111528-54855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-23256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111531-62406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111531-59718.png)
⑤在正项等比数列
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111529-12947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111531-79252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111531-89632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111510-49777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111510-98277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111510-91270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111510-38579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-40281.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-83553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-85068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-95896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-73691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-49670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111511-64991.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111512-87230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111512-78484.png)
(2)求PC与平面PAD所成角的正弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111512-22973.png)
![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-37306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-49701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-69367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-56107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-41875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-93789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-16891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-72524.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-76278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111449-37306.png)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-50449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111450-23064.png)
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