名校
1 . 已知A,B是平面内两个定点,且
,点集
.若M,
,则向量
、
夹角的余弦值的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42083f00cd68320e4e0275400c139551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6baeb59466a29c08f6d28314b7dd0a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf441d5a9df0c4cf99923082cbed07e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8962b0c33df0302e741501c1491bf643.png)
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2023-11-23更新
|
748次组卷
|
4卷引用:上海市大同中学2023-2024学年高三上学期期中考试数学试卷
上海市大同中学2023-2024学年高三上学期期中考试数学试卷上海市建平中学2024届高三下学期3月考试数学试题(已下线)重难点4-1 平面向量的最值与范围(4题型+满分技巧+限时检测)(已下线)第05讲 6.2.4向量的数量积(2)-【帮课堂】(人教A版2019必修第二册)
23-24高三上·上海浦东新·期中
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解题方法
2 . 已知
满足
,且
,则
在
上数量投影的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9c91af174ebe66c921f52db385a6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4821b88f7ff6296126e9e29260b3ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6234d132ead5cf8194883f1b3fe22622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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3 . 已知平面向量
,
满足
,
且向量
,
的夹角为
,则
在
方向上的数量投影为______ .
![](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/3aa3610a990287d3ac756abae406540d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e405db6c09d6ab5739cabbb63cd3b3bd.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/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa3e1ce447d158f6084a66841307a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
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4 . 设
分别是双曲线
的左、右焦点,
为坐标原点,第一象限内的点
在
的右支上,且
,则
的内心坐标为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e6bb54af35fd692a472b23c9f4694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1374ea85d96d9eaf6b4f022ae02e8a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
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5 . 已知
,
与
垂直,
,且
与
的夹角是钝角,则
在
方向上的投影为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5703cc339983ceadf441ba9df493d910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a4fe23b799a0777b2faebd77dd05bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2941c96f6bfbc0ca5e4940ba02b05d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
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6 . 已知向量
,则
在
方向上的数量投影为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca807ba285f443599e298ba4ee393132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2023-04-02更新
|
821次组卷
|
3卷引用:上海市进才中学2023届高三下学期3月月考数学试题
解题方法
7 . 已知四边形ABCD是平行四边形,若
,
,
,且
,则
在
上的数量投影为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6186503c922e2bf1868927d4ff103928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640e5f20dc31406de1e00cb7fd30480f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e192dd7e5f73009a5ac1e407d2a4e333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0aeea7f7c6368f30e2c815e0ebefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c3accb1b8a5479439beff4259660e3.png)
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解题方法
8 . 已知平面向量
、
满足
,
,则
在
方向上的数量投影的最小值是______ .
![](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/3aa3610a990287d3ac756abae406540d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e405db6c09d6ab5739cabbb63cd3b3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa3e1ce447d158f6084a66841307a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
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2022-12-16更新
|
1077次组卷
|
4卷引用:上海市宝山区2023届高三上学期一模数学试题
上海市宝山区2023届高三上学期一模数学试题(已下线)专题5-1 平面向量中的高频小题归类-3上海市上海师范大学附属中学2022-2023学年高二下学期3月月考数学试题(已下线)6.2 平面向量的运算(精讲)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)
解题方法
9 . 在边长为2的正六边形ABCDEF中,点P为其内部或边界上一点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a99dd213bd9e8160fd9a5b7f12aecf.png)
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解题方法
10 . 如图,
、
是以
为直径的圆上的两点,其中
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/c8d25949-7e3d-420f-b767-3712887c7c39.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f0f7375222b479e96c7d536db7c9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecb2fb4a81ac06a13be4436edc098be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c0098e82d41438224ce472054e5490.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/c8d25949-7e3d-420f-b767-3712887c7c39.png?resizew=145)
A.1 | B.2 | C.![]() | D.![]() |
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2023-02-16更新
|
2018次组卷
|
3卷引用:上海市上海中学2022届高三下学期高考模拟3数学试题