题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-98696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-30514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-38792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-87641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-82877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-76789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-48310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-84228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-33135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-45997.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-30514.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-47286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-68904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-98696.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-63572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020435-67696.png)
解析
试题分析:(1)先根据平面向量垂直的等价条件得到等式
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020435-63420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020435-33278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-30514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-30514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020435-20261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020436-57897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020436-96872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020436-15324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020436-62487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-98696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-48310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020433-48310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020437-64835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-98696.png)
试题解析:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-45997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020437-37413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020435-63420.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020437-12360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020437-55003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020438-57669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-63572.png)
(2)解法一:由正弦定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020438-84621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-47286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-68904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-63572.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020438-17694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020432-98696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020438-78854.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020438-62444.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020439-96927.png)
解法二:因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-47286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-68904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020434-63572.png)
所以由余弦定理可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020439-77551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020439-82958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020439-35720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020440-65192.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020439-35720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020440-65836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020440-12509.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020440-65192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020440-13502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020441-50065.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020441-35645.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020425-20240.png)
A.![]() | B.![]() | C.1 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020411-22301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020411-97428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020412-36511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020412-67236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020412-42895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020413-69309.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020413-60351.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020413-89124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020413-28100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020413-92419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020414-17648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020414-69491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020404-55330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020404-89003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020405-71908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020405-34380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020405-96062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020404-89003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020405-40931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020404-89003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020406-83697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020406-96413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020406-86098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020407-81583.png)
(1)求线段
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020406-83697.png)
(2)若以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020407-98942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020407-98942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020404-89003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020407-98942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-19672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-98436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-71724.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020339-48986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020339-18350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020339-47018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020340-61707.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020339-18350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020338-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020340-89421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020340-29888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020340-67351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020341-58747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020341-52129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020341-32155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020330-57181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020331-82321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020331-31398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020331-74893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020331-76580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020331-88046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020332-33687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020332-26785.png)
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