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科目:高中數(shù)學(xué)
來源:
題型:
設(shè)
=(-2,2,5),=(6,-4,4)分別是平面α,β的法向量,則平面α與β的夾角為( �。�
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科目:高中數(shù)學(xué)
來源:
題型:
已知平面向量
與
的夾角為
,|
|=
,|
|=1,則|
-
|=
;若平行四邊形ABCD滿足
=
+
,
=
-
,則平行四邊形ABCD的面積為
.
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科目:高中數(shù)學(xué)
來源:2011-2012學(xué)年廣東省外語外貿(mào)大學(xué)附設(shè)外語學(xué)校高三(上)數(shù)學(xué)寒假作業(yè)3(文科)(解析版)
題型:選擇題
關(guān)于平面向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/0.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/1.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/2.png)
.有下列三個(gè)命題:
①若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/3.png)
•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/5.png)
•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/6.png)
,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/7.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/8.png)
.
②若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/9.png)
=(1,k),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/10.png)
=(-2,6),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/11.png)
∥
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/12.png)
,則k=-3.
③非零向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/13.png)
和
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/14.png)
滿足|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/15.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/16.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/17.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/18.png)
|,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/19.png)
與
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/20.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101232018465802497/SYS201311012320184658024002_ST/21.png)
的夾角為60°.
其中真命題的個(gè)數(shù)有( )
A.0
B.1
C.2
D.3
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科目:高中數(shù)學(xué)
來源:2011-2012學(xué)年安徽省六安市壽縣一中高三(上)第四次月考數(shù)學(xué)試卷(理科)(解析版)
題型:填空題
關(guān)于非零平面向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/0.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/1.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/2.png)
.有下列命題:
①若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/3.png)
=(1,k),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/4.png)
=(-2,6),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/5.png)
∥b,則k=-3; ②若|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/6.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/7.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/8.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/9.png)
|,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/10.png)
與
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/11.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/12.png)
的夾角為60°;
③|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/13.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/14.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/15.png)
|+|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/16.png)
|?
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/17.png)
與
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/18.png)
的方向相同; ④|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/19.png)
|+|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/20.png)
|>|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/21.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/22.png)
|?
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/23.png)
與
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/24.png)
的夾角為銳角;
⑤若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/25.png)
=(1,-3),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/26.png)
=(-2,4),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/27.png)
=(4,-6),則表示向量4
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/28.png)
,3
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/29.png)
-2
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/30.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231601337748233/SYS201311012316013377482014_ST/31.png)
的有向線段首尾連接能構(gòu)成三角形.
其中真命題的序號(hào)是
(將所有真命題的序號(hào)都填上).
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科目:高中數(shù)學(xué)
來源:《2.1-2.2 平面向量的概念及其線性運(yùn)算》2011年同步練習(xí)(解析版)
題型:填空題
關(guān)于平面向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/0.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/1.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/2.png)
,有下列三個(gè)命題:
①若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/3.png)
•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/5.png)
•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/6.png)
,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/7.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/8.png)
、
②若
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/9.png)
=(1,k),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/10.png)
=(-2,6),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/11.png)
∥
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/12.png)
,則k=-3.
③非零向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/13.png)
和
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/14.png)
滿足|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/15.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/16.png)
|=|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/17.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/18.png)
|,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/19.png)
與
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/20.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101221751221882110/SYS201311012217512218821009_ST/21.png)
的夾角為60°.
其中真命題的序號(hào)為
.(寫出所有真命題的序號(hào))
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