题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022544-69463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022544-23255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022544-92547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022544-55659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022544-95093.png)
(1)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-14915.png)
(2)能否以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-72935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-59592.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-22439.png)
解析
(1)假设四点共面,则存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-91830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-15069.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-73397.png)
(2)利用不同面的三个向量可以充当空间的基底,那么我们可以得到,判定
解:(1)假设四点共面,则存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-91830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-15069.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-73397.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022546-85347.png)
比较对应的系数,得一关于
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-91830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022546-69288.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022546-92775.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-73397.png)
(2)若向量
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022546-57036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022547-94627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022547-62640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022547-34755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022548-25992.png)
同(1)可证,这不可能,
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-72935.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022548-79450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022548-69240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022548-13306.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022548-40891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022549-50373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022549-87144.png)
从中解得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022549-44058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022545-22439.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022536-82768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022536-47019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022537-49161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022537-25822.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022536-82768.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022537-68886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022537-29801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022538-95217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022538-59045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022538-59045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022537-68886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022530-90757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022530-61769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022531-61749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022531-11152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022531-90634.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022532-74975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022532-20964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022532-17666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022526-18290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022526-85021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022526-58004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022527-82086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022527-67127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022526-58004.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022527-97476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022527-90929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022516-14002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022516-68400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022516-71375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022509-73642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022510-90071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022510-52353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022509-73642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105022510-43591.png)
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