题目内容
已知向量
=(
),
=(
).
(1)当
时,求
的值。
(2)已知
=
,
求
的值。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403349288.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403364583.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403380324.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403411604.png)
(1)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403442796.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403458439.png)
(2)已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403458439.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403505318.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144035201023.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403567452.png)
(1)
(2)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144039881124.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403661586.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403879461.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144039881124.png)
本试题主要考查了向量的数量积的运算,以及构造角求解三角函数值的运用。
第一问中,利用
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144040972154.png)
第二问中,结合第一问中
=
然后
,构造角
得到结论。
解、(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144042382147.png)
(2)
因为:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214404285970.png)
=
所以:
因为:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144043631880.png)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144039881124.png)
第一问中,利用
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144040972154.png)
第二问中,结合第一问中
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144041131384.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403505318.png)
然后
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144041601444.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144042071597.png)
解、(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144042382147.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214404253168.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214404285970.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144043001390.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823214403505318.png)
所以:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144041601444.png)
因为:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144043631880.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144043781614.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232144039881124.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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