题目内容
若非零向量a, b满足(a+3b)⊥(7a-5b),(a-4b)⊥(7a-2b),求a,b的夹角。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823211958209382.png)
运用向量的数量积,利用垂直关系,求向量的夹角.
解:因为(a+3b)⊥(7a-5b),(a-4b)⊥(7a-2b)
因此有
,
…………….2分
…………….6分
cos<a, b >=
,a,b的夹角为
…………….12分
解:因为(a+3b)⊥(7a-5b),(a-4b)⊥(7a-2b)
因此有
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823211958240930.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823211958287920.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232119583031476.png)
cos<a, b >=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823211958334756.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823211958209382.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目