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由空间向量基本定理可知,空间任意向量可由三个不共面的向量唯一确定地表示为,则称(...
由空间向量基本定理可知,空间任意向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/0.png)
可由三个不共面的向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/1.png)
唯一确定地表示为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/2.png)
,则称(x,y,z)为基底
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/3.png)
下的广义坐标.特别地,当
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/4.png)
为单位正交基底时,(x,y,z)为直角坐标.设
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/5.png)
分别为直角坐标中x,y,z正方向上的单位向量,则空间直角坐标(1,2,3)在基底
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898012_ST/6.png)
下的广义坐标为
.
考点分析:
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我们知道,在平面直角坐标系中,方程
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/0.png)
表示的图形是一条直线,具有特定性质:“在x轴,y轴上的截距分别为a,b”;类比到空间直角坐标系中,方程
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/1.png)
表示的点集对应的图形也具有某特定性质,设此图形为m,若m与zoy平面所成角正弦值为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/2.png)
,则正数λ的值是( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/3.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/4.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898011_ST/5.png)
D.
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如图,矩形ABCD的长AB=2,宽AD=x,若PA⊥平面ABCD,矩形的边CD上至少有一个点Q,使得PQ⊥BQ,则x的范围是( )
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898010_ST/images0.png)
A.0<x≤1
B.0<x≤2
C.1<x≤2
D.x≥1
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有一个长方体容器ABCD-A
1B
1C
1D
1,装的水占恰好占其容积的一半;α表示水平的桌面,容器一边BC紧贴桌面,沿BC将其翻转使之略微倾斜,最后水面(阴影部分)与其各侧棱的交点分别是EFGH(如图),设翻转后容器中的水形成的几何体是M,翻转过程中水和容器接触面积为S,则下列说法正确的是( )
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898009_ST/images0.png)
A.M是棱柱,S逐渐增大
B.M是棱柱,S始终不变
C.M是棱台,S逐渐增大
D.M是棱台,S积始终不变
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异面直线a,b所成角为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/0.png)
,直线c⊥a,且c也与b异面,则直线b与c所成的角的范围为( )
A.[
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/1.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/2.png)
]
B.[
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/3.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/4.png)
]
C.[
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/5.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/6.png)
]
D.[
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898008_ST/7.png)
,
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]
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空间作用在同一点的三个力
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/0.png)
两两夹角为60°,大小分别为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/1.png)
,设它们的合力为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/2.png)
,则( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/3.png)
,且与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/4.png)
夹角余弦为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/5.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/6.png)
,且与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/7.png)
夹角余弦为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/8.png)
C.
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,且与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/10.png)
夹角余弦为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/11.png)
D.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101936722589882/SYS201311031019367225898007_ST/12.png)
,且与
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夹角余弦为
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