题目内容
(本题满分13分)
如图,已知ΔABO中,点C为线段AB中点,点D
是线段OB上的点,且
,AD和OC交于点E,
设
.
(1)用
表示向量
;
(2)若
,求实数
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422801962.gif)
是线段OB上的点,且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422832369.gif)
设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422848540.gif)
(1)用
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422863243.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422879338.gif)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422895691.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422910343.gif)
(1)∵C为AB中点,∴
.
∵
∴
∴
(2)在ΔOEA中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423113861.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082318342330072.gif)
,
.
(本题方法多样,只要说理充分都给分)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422926589.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422941967.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183422832369.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423035384.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423051525.gif)
(2)在ΔOEA中,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423066500.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423097588.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423113861.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423129129.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423222489.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423238543.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423253455.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423269475.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082318342330072.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423316295.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823183423331399.gif)
(本题方法多样,只要说理充分都给分)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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