题目内容
(本题14分)已知空间
三点A(0,2,3),B(-2,1,6),C(1,-1,5)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316324899328654.jpg)
⑴求以向量
为一组邻边的平行四边形的面积S;
⑵若向量
分别与向量
垂直,且
=
,求向量
的坐标。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316324891572.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316324899328654.jpg)
⑴求以向量
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249008335.gif)
⑵若向量
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249039203.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249008335.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249071231.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249102225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249039203.gif)
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249149775.gif)
(2)a=(1,1,1), a=(-1,-1,-1).
解:⑴![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231632491641325.gif)
∴∠BAC=60°,![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249149775.gif)
⑵设a=(x,y,z),则![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249211649.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231632492271201.gif)
解得x=y=z=1或x=y=z=-1,∴a=(1,1,1), a=(-1,-1,-1).
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231632491641325.gif)
∴∠BAC=60°,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249149775.gif)
⑵设a=(x,y,z),则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823163249211649.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231632492271201.gif)
解得x=y=z=1或x=y=z=-1,∴a=(1,1,1), a=(-1,-1,-1).
![](http://thumb2018.1010pic.com/images/loading.gif)
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