已知
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_ST/0.png)
,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_ST/1.png)
与
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_ST/2.png)
的夹角为45°,若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_ST/3.png)
,则实数λ的取值范围是
.
【答案】
分析:由
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/0.png)
可得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/1.png)
,展开且把已知代入可得,λ
2+2λ-3<0,解不等式可求λ的范围
解答:解:∵
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/2.png)
,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/3.png)
与
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/4.png)
的夹角为45
又∵
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/5.png)
∴
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/6.png)
即
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/7.png)
把已知代入可得,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/8.png)
∴λ
2+2λ-3<0
解不等式可得,-3<λ<1
故答案为:(-3,1).
点评:本题主要考查了平面向量的数量积的定义
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/9.png)
及性质
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230456888130754/SYS201311012304568881307012_DA/10.png)
的应用,从而把向量的运算转化为数的基本运算.
练习册系列答案
相关习题
科目:高中数学
来源:2009-2010学年重庆市南开中学高三(上)1月月考数学试卷(理科)(解析版)
题型:填空题
已知
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230418832560283/SYS201311012304188325602012_ST/0.png)
,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230418832560283/SYS201311012304188325602012_ST/1.png)
与
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230418832560283/SYS201311012304188325602012_ST/2.png)
的夹角为45°,若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131101230418832560283/SYS201311012304188325602012_ST/3.png)
,则实数λ的取值范围是
.
查看答案和解析>>
科目:高中数学
来源:2008-2009学年浙江省宁波市镇海中学高三(上)期中数学试卷(文科)(解析版)
题型:填空题
查看答案和解析>>
科目:高中数学
来源:2010年浙江省台州市高考数学一模试卷(理科)(解析版)
题型:填空题
已知
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125949669603921/SYS201310251259496696039010_ST/0.png)
,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125949669603921/SYS201310251259496696039010_ST/1.png)
与
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125949669603921/SYS201310251259496696039010_ST/2.png)
的夹角为45°,若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125949669603921/SYS201310251259496696039010_ST/3.png)
,则实数λ的取值范围是
.
查看答案和解析>>
科目:高中数学
来源:2010年四川省广安二中高三一诊复习数学试卷(三)(解析版)
题型:填空题
已知
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125349077046487/SYS201310251253490770464013_ST/0.png)
,
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125349077046487/SYS201310251253490770464013_ST/1.png)
与
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125349077046487/SYS201310251253490770464013_ST/2.png)
的夹角为45°,若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025125349077046487/SYS201310251253490770464013_ST/3.png)
,则实数λ的取值范围是
.
查看答案和解析>>