题目内容
已知A(-1,2),B(2,8).
(1)若
=![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022272317.png)
,
=-![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022319394.png)
,求
的坐标;
(2)设G(0,5),若
⊥
,
∥
,求E点坐标.
(1)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022257472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022272317.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022288442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022304449.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022319394.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022288442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022350458.png)
(2)设G(0,5),若
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022366481.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022397456.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022413458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022397456.png)
(1)
=(1,2) (2)![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022491803.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022350458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022491803.png)
本试题主要考查了向量的运算。
(1)∵
=(3,6),
=![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022272317.png)
=(1,2),
=-![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022319394.png)
=(-2,-4), 2分
∴C(0,4),D(1,6),∴
=(1,2). 6分
(2)设E(x,y),则
=(x+1,y-2),
=(x-2,y-8),
∵
=(-2,-3),
⊥
,
∥
,
∴
10分
∴E点坐标为
.
(1)∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022288442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022257472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022272317.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022288442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022304449.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022319394.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022288442.png)
∴C(0,4),D(1,6),∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022350458.png)
(2)设E(x,y),则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022366481.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022413458.png)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022397456.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022366481.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022397456.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022413458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022397456.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232130228812170.png)
∴E点坐标为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823213022491803.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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