题目内容
已知向量
,且与向量
的夹角为
,其中
是
的内角.
(1)求角
的大小;
(2)求
的取值范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507376827.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507391491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507391389.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507407521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507423544.png)
(1)求角
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507438309.png)
(2)求
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507454584.png)
解:(1)∵
, 且与向量
所成角为
∴
,
∴
,∴
∴
又
, ∴![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507672613.png)
第一问:另解: ∵
, 且与向量
所成角为
∴
(2)由(1)可知
所以
∵
∴
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035079221168.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507501859.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507516541.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507532447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507547164.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035075631538.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507594719.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507610716.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507625784.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507657549.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507672613.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507688173.png)
第一问:另解: ∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507703817.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507719531.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507532447.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035077661103.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035077811654.png)
(2)由(1)可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507797653.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035078131028.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035078281311.png)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507844603.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507859740.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823203507547164.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035079061274.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232035079221168.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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