题目内容
(12分) 已知向量
与
的夹角为30°,且|
|=
,|
|=1,(1)求|
-2
|的值;(2)设向量
=
+2
,
=
-2
,求向量
在
方向上的投影.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044962204.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044977202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044962204.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045024217.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044977202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044962204.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044977202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045133212.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044962204.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044977202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045211208.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044962204.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123044977202.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045133212.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045211208.gif)
(Ⅰ) 1 (Ⅱ) ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045320141.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045320141.gif)
:(1) ∵|
-2
|=
=
=
="1 " 6分
(2) 法一:由(1)可知
;
;![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045508532.gif)
∴
=
=
从而在方向上的投影为
12分
(法二):∵由(1)可知
;
=
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045648291.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045336203.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045367203.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045414502.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045430624.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045445563.gif)
(2) 法一:由(1)可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045476529.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045492664.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045508532.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045523480.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045539424.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045554320.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045570594.gif)
(法二):∵由(1)可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045476529.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045601552.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045632504.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123045648291.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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