名校
1 . 已知点
在
所在的平面内,则下列各结论正确的个数是________ .
①若
为
的垂心,
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3b155f027cff2b2227011eb10be484.png)
②若
为边长为2的正三角形,则
的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
③若
,则动点
的轨迹经
的外心
④若
为
的重心,过点
的直线
分别与
、
交于
、
两点,若
,
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2596ac1a8301e39179b80fbd3bd3169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3b155f027cff2b2227011eb10be484.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7a9bb8ba3d2ec7d9ccb5f6c76abfd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e616355594732c3e0dbf8c86a683b4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/4e4425dc7c346e4597c0521d7f636174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3605b320cae7b4a85aa273dfb7e606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d3718ecdc213d626b9ee1525cd2aa8.png)
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名校
2 . 已知两个不相等的非零向量
,
,满足
,且
与
的夹角为
,则
的取值范围是________ .
![](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/e2396cac4b185cf1f1a67dad9248481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3143307ad0ba4a631eac04e814993655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996bf3d35b6763cbc1a423b13a9df2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6fbff85947f4df50ae1b17e967a158.png)
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名校
解题方法
3 . 已知
,向量
在
上的投影向量为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd01707e8d32f277b83c007a5b15bd7.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6316d995f00623f05fc3d56a6cbe5f00.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/15993be27378b82b70a703884d7ae027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd01707e8d32f277b83c007a5b15bd7.png)
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2023-04-20更新
|
678次组卷
|
3卷引用:河北省承德市重点高中2022-2023学年高一下学期期中联考数学试题
名校
4 . 已知向量
和
满足
,则
在
方向上的数量投影为___ .
![](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/ed8b2336a25d41cb33b01ceadcb1e51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2023-03-28更新
|
316次组卷
|
2卷引用:河北省衡水市第二中学2022-2023学年高一下学期期中数学试题
名校
解题方法
5 . 已知向量
,
的夹角为
,
,则向量
在
方向上的投影为 __ .
![](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/b4beecc07043ee0a0d463480c262007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d02c32d073ad9cd506ef84c3698780.png)
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2022-11-25更新
|
996次组卷
|
6卷引用:河北省衡水金卷先享题2022-2023学年高三上学期理科模拟数学试题(二)
河北省衡水金卷先享题2022-2023学年高三上学期理科模拟数学试题(二)(已下线)6.2 平面向量的运算(学案)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)6.2.4 向量的数量积 (精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)四川省绵阳市2023届高三上学期二诊模拟考试数学(理)试题四川省泸县第一中学2023-2024学年高三上学期10月月考数学(文)试题四川省泸县第一中学2023-2024学年高三上学期10月月考数学(理)试题
名校
6 . 如图,在正六边形ABCDEF中,向量
在向量
上的投影向量是
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6531a6dd69228f455d29ad8b0f133d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/6e26faec-8ac7-420e-a877-ebfebe1fbe04.png?resizew=119)
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2022-12-19更新
|
535次组卷
|
8卷引用:河北省沧衡八校联盟2022-2023学年高一下学期期中数学试题
7 . 剪纸艺术是一种中国传统的民间工艺,它源远流长,经久不衰,已成为世界艺术宝库中的一种珍藏.某学校为了丰富学生的课外活动,组织了剪纸比赛,小明同学在观看了2022年北京冬奥会的节目《雪花》之后,被舞台上一片片漂亮的“雪花”所吸引,决定用作品“雪花”参加剪纸比赛.小明的参赛作品“雪花”如图1所示,它的平面图可简化为图2的平面图形,该平面图形既是轴对称图形,又是中心对称图形,其中,
为该平面图形上的一个动点(含边界),六边形
为正六边形,
,
,
为等边三角形,则
的最大值为________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/8f1a6b20-f87b-4db2-8280-02b815be2921.png?resizew=125)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb6b85a1556909e20230cb5eda97e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a70703a7d028256aee709f4d616434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42e90b10627ce4adfe97c633648022f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbcf9643811f624dcf54112966a0502c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/8f1a6b20-f87b-4db2-8280-02b815be2921.png?resizew=125)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/bcae322e-8009-4b9f-81fc-a5940d0cbc0f.png?resizew=146)
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2022-06-27更新
|
523次组卷
|
4卷引用:河北省承德高中2021~2022学年高一下学期六月联考数学试题
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解题方法
8 . 在等腰梯形ABCD中,
,
,点P为BC中点,点Q是边AB上一个动点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641aa755ada1d83daafc82d5f1fa88db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97b5a5f3853f0ac8712decba0c0a4.png)
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2022-04-30更新
|
443次组卷
|
2卷引用:河北省2022届高三下学期4月全过程纵向评价数学试题
名校
9 . 已知
,
,
是非零平面向量,
,
,
,
,则
的最大值是_________ .
![](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/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18996bd00253c3ad9f91780103affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94132c0a84504da22f25b780ca9e733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6860a705b488c938da26221e43e60487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb1145d523ca1416cdcdf5ba91dd905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7302b2c1d628ee4b565fb3d5f9c7a8cf.png)
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2022-03-24更新
|
2085次组卷
|
5卷引用:河北省泊头市第一中学2021-2022学年高一下学期第一次月考数学试题
河北省泊头市第一中学2021-2022学年高一下学期第一次月考数学试题浙江省温州市2022届高三下学期3月高考适应性测试数学试题(已下线)专题17 向量中的隐圆问题(已下线)专题25 圆中的范围与最值问题-2(已下线)第05讲 平面向量的数量积(一)
名校
10 . 已知向量
,
.若向量
在向量
方向上的投影为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1749b03f44697b61f4d2f408dece3e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6c14d7c17db8676f3007d53a41dbf8.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/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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2022-03-20更新
|
669次组卷
|
3卷引用:河北省滦平县第一中学2023届高三下学期2月月考数学试题