2023·江苏南通·模拟预测
名校
解题方法
1 . 已知非零向量
,
满足
,且
在
上的投影向量为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f1100340bc2283937d44abaabc28a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5229e91d34d5f4814de8fc7232d9fe58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06e744cba89ec01188e63b5d45ffffe.png)
A.![]() | B.![]() | C.2 | D.![]() |
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7卷引用:湖北省荆州市松滋市第一中学2024届高三上学期12月月考模拟数学试题(二)
湖北省荆州市松滋市第一中学2024届高三上学期12月月考模拟数学试题(二)(已下线)江苏省南通市如皋市2023届高三下学期适应性测试(三)数学试题(已下线)第01讲 平面向量专题期末高频考点题型秒杀江苏省镇江中学2023届高三三模数学试题江苏省苏州市苏州中学2022-2023学年高一下学期6月月考数学试题2024届河南省信阳市浉河区信阳高级中学二模数学试题广东省广州市铁一中学2023-2024学年高一下学期3月月考数学试题
2 . 已知点
分别为直线
上的动点,若
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788ec53cbee00208c2524390c2ffd2d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c7f170dfc9f5f2e76eae7ea26a82d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91942670354affa8d52edadbcfa762bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-08更新
|
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3卷引用:湖北省荆州市沙市中学2023届高三下学期6月适应性考试数学试题
名校
3 . 已知向量
,
,
与
的夹角为
,若对任意
,当
时,
恒成立,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9338520b3ccd2d16e0db9acf8fdd1465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf342e77c56e55a35bb1151bc215a3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d107ada5b88073d42481ba8dce1316de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b643b9d314f1f0a84235822e11c63366.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-03更新
|
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2卷引用:湖北省沙市中学2022-2023学年高二下学期5月月考数学试题
名校
解题方法
4 . 如图,四棱锥P-ABCD中,底面ABCD是边长为3的正方形,
,AP与AB,AD的夹角都是60°,若M是PC的中点,则直线MB与AP所成角的余弦值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602ee324ca5bc3cf9ef251a061b431ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/29/734e0afc-cb94-4f09-a13a-33620b230ae6.png?resizew=158)
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4卷引用:湖北省沙市中学2022-2023学年高二下学期5月月考数学试题
解题方法
5 . 已知
分别为
的内角
所对的边,
,且
.
(1)求
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7315d701498c8f688b8981d4ec629b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c84e49bfcc71b8c7d2113230af7321.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7be1eb90c14d19a7cc66e8b90b7af89.png)
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3卷引用:湖北省荆州市部分校2022-2023学年高一下学期期中联考数学试题
名校
解题方法
6 .
中,BC边上的点D满足
,
,点G在三角形内,满足
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e4749d7c41abc0f5b8d1c441b647ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612d9156dc505c0fdc9640ebbe4f76be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147ab2d582e60bee6d81b27236e7288b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3f5457c71b8a0a8f276125184947b0.png)
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4卷引用:湖北省荆州市公安县第三中学2022-2023学年高一下学期5月月考数学试题
湖北省荆州市公安县第三中学2022-2023学年高一下学期5月月考数学试题河南省郑州外国语学校2022-2023学年高一下学期第一次月考数学试题(已下线)高一数学下学期期中模拟试题01(平面向量、解三角形、复数、立体几何)(已下线)第五篇 向量与几何 专题13 奔驰定理 微点2 奔驰定理(二)
名校
解题方法
7 . 设
,
是不共线的两个向量,若
,
,
.
(1)若
,
,且
,求
与
的夹角
;
(2)若A,B,C三点共线,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bacd34871282154e6621171d64f7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1002fcd7b1321ee5893c90283b5bcc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3569431df08163b781c78b63ab530df8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54078c4af5b305e26b8e3faa6423e67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b982e3d8f4df04309a922a4872dac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13653b0632c26d9d25d1a131e05330b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若A,B,C三点共线,求m的值.
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2023-03-31更新
|
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|
3卷引用:湖北省荆州市部分校2022-2023学年高一下学期期中联考数学试题
名校
解题方法
8 . 已知向量
,
,
.若
与
垂直,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5463fb0b7d03747aa4d680620ca81be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0979ead3a09ede4835e7fe77c87850f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53dec1d306c6f467257184d11baa451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3956599a5821a2018992785421abe720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.2 | D.![]() |
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7卷引用:湖北省沙市中学2022-2023学年高一下学期5月月考数学试题
名校
9 . 已知平面向量
,
满足
,
,并且当
时,
取得最小值,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7c6e69895574db29f6326bd82f21e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404067afb19bd74f447a6c0c832af1da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9fde8d670b8d1bc619f5722467a87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2fa77da3a803251ab7a62214d00455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd135b98371091fc7cd40b6435caf1a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:湖北省荆州市松滋一中2024届高三上学期12月月考数学试题
名校
10 . 如图,在平面四边形
中,
,
,
,
,
、
分别是
,
的中点,
为线段
上一点,且
.设
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/21/86d9effa-030e-4033-81ec-e422e76bc569.png?resizew=187)
(1)若
,以
,
为基底表示向量
与
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf4ec2987f0a536119cbae7bd3e0213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/21/86d9effa-030e-4033-81ec-e422e76bc569.png?resizew=187)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b8a2a41a8b50e10d68943e3f0f4e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ed82f6aba5e5e5f896de9571233c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4e73380e6dc09aa00aa6738eeb46df5.png)
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|
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6卷引用:湖北省沙市中学2022-2023学年高一下学期5月月考数学试题
湖北省沙市中学2022-2023学年高一下学期5月月考数学试题河北省邯郸市2021-2022学年高一下学期期末数学试题江苏省如皋市长江高级中学、淮安市南陈集中学2022-2023学年高一下学期3月联考数学试题(已下线)9.3.1 平面向量基本定理-【题型分类归纳】2022-2023学年高一数学同步讲与练(苏教版2019必修第二册)(已下线)6.3.1 平面向量基本定理(精讲)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)期末专题04 平面向量大题综合-【备战期末必刷真题】