题目内容
(本小题满分12分)设
,
是两个相互垂直的单位向量,且
,
.
(1)若
,求
的值;
(2)若
,求
的值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649195303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649211337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649227690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649242608.png)
(1)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649273454.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649289323.png)
(2)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649367432.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649289323.png)
解法一:(1)由
,且
,故存在唯一的实数
,使得
,
即![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650116826.png)
…6分
(2)
,
,即![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650225915.png)
,
,
…12分
解法二:∵
,
是两个相互垂直的单位向量,
∴
、
, …4分
⑴∵
,∴
,解得
; …8分
⑵
,
,即
,解得
。…12分
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649273454.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649695427.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649913337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649960521.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650116826.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650163996.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650178475.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650209497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650225915.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231956502411019.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650256539.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650319451.png)
解法二:∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649195303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649211337.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650553864.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650584789.png)
⑴∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195649273454.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650693770.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650709498.png)
⑵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650178475.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650209497.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650787774.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195650802429.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目