真题
1 . 在边长为1的正方形
中,点
为线段
的三等分点,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ ;
为线段
上的动点,
为
中点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f8c08d4be8d309dc82fd4b170db11b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c98a41ef6f9c38a7ebfc74dde60853.png)
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2 . 四边形ABCD中,
,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791666b74a5c0260017e12060c3cc06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764b88d918c3b2dca6587af4893ad08b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253374ac677c35bf4d1dc260d688b63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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2024-04-26更新
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272次组卷
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5卷引用:2024年天津高考数学真题平行卷(基础)
(已下线)2024年天津高考数学真题平行卷(基础)(已下线)北京市中国人民大学附属中学2023-2024学年高一下学期期中练习数学试题变式题11-15(已下线)专题01 向量基底、四心及其应用(2)-期末考点大串讲(苏教版(2019))北京市中国人民大学附属中学2023-2024学年高一下学期期中练习数学试题黑龙江省大庆市大庆中学2024届高三下学期5月期中数学试题
名校
解题方法
3 . 在
中,M是边BC的中点,N是线段BM的中点.设
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
__________ ;若
,
的面积为
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
__________ 时,
取得最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc51bdc8c2c18379db1affbb06f8923f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06393c604df2200ce9fd4bc9e67c2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
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2024-03-01更新
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1447次组卷
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6卷引用:信息必刷卷04(天津专用)
(已下线)信息必刷卷04(天津专用)(已下线)2024年天津高考数学真题平行卷(提升)天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷天津市实验中学滨海学校2023-2024学年高一下学期随堂质量监测(月考)数学试题(已下线)压轴题03不等式压轴题13题型汇总 -1(已下线)第2套 新高考新结构全真模拟2(艺体生)
解题方法
4 . 在平行四边形
中,
,
是
的中点,
,若设
,则
可用
,
表示为__________ ;若
的面积为
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fa6107a40510334d4dfa875b94c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32905649969178ac0426c6186627948d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7d3a0680780aaf4549c447fe8dfe9f.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/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ed421edfa196cb03a2521d0170e1ca.png)
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2024-01-25更新
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777次组卷
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4卷引用:2024年高考数学二轮复习测试卷(天津专用)
(已下线)2024年高考数学二轮复习测试卷(天津专用)天津市宁河区2024届高三上学期期末数学试题(已下线)考点5 平面向量的应用 --2024届高考数学考点总动员【练】天津市武清区杨村第三中学2023-2024学年高一下学期第一次过程性评价数学试题
5 . 如图,在
中,
,过点
的直线分别交直线
于不同的两点
,记
,用
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56f0466c67eb5811da543f2959b403f.png)
______ ;设
,若
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd1102eb2ccdb8d722c43333944af08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ba495e8f9fe02229a4248fdbfb4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56f0466c67eb5811da543f2959b403f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aa9e08e415270c69b956cca8b0a431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ea271b3352d75008832f129d39dc0.png)
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2024-01-16更新
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1791次组卷
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9卷引用:2024年天津高考数学真题变式题11-15
(已下线)2024年天津高考数学真题变式题11-15天津市和平区2024届高三上学期期末质量调查数学试题(已下线)经典好题1 积常和小 和常积大【练】(已下线)专题9.4 平面向量基本定理-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)热点4-1 平面向量的概念、线性运算与基本定理(6题型+满分技巧+限时检测)(已下线)6.3.1平面向量基本定理-高频考点通关与解题策略(人教A版2019必修第二册)天津市嘉诚中学2023-2024学年高一下学期第一次月考数学试卷(已下线)期末模拟卷(范围:人教A版2019必修第二册)-期末真题分类汇编(天津专用)(已下线)6.3.1 平面向量基本定理——课后作业(基础版)
名校
6 . 如图,在
中,
,
,CD与BE交于点P,
,
,
,则
的值为_______ ;过点P的直线l交AB,AC于点M,N,设
,
(
,
),则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e7376fefe18d435f4adbb6226d7aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f09a9d6f118c19854f944a8a258b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3169672a04283c85f61d2e7be2172fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fa908112806dc176b8abdc3b3aaa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a93a467f11c29aa3ec6124398b1c5a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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2023-11-12更新
|
855次组卷
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4卷引用:黄金卷02
(已下线)黄金卷02天津市南开中学2024届高三上学期统练8数学试题(已下线)第06讲 6.3.1平面向量基本定理-【帮课堂】(人教A版2019必修第二册)天津市蓟州区第一中学2024届高三第一次校模拟考数学试卷
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解题方法
7 . 在边长为2的菱形
中,
,若
为
的中点,则
值为__________ ;若点
为
边上的动点,点
是
边上的动点,且
,
,
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4452db7f56b15dbeb9bddb30740eb07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/4e4425dc7c346e4597c0521d7f636174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc04f80ff09e15ca9fcb1ec3d88a02b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3ede869e508a8c8bda34a16782f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62766bb3748a2775a7a0b9ccc6313d84.png)
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8 . 已知平面向量
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6234d132ead5cf8194883f1b3fe22622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b8583acf0b89997429dbbaa837c3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f6f71602e479f2db73deab897b5224.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 窗花是贴在窗子或窗户上的剪纸,是中国古老的传统民间艺术之一,图1是一个正八边形窗花隔断,图2是从窗花图中抽象出的几何图形的示意图.如图2,正八边形ABCDEFGH内角和为1080°,若
(
,
),则
的值为____________ ;若正八边形ABCDEFGH的边长为2,P是正八边形ABCDEFGH八条边上的动点,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c453c3b096207222485c01cb0a6059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cefeddff52b02a43831beeb4bb6faa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83b9f01e806bf74042ba41b26423022.png)
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2023-08-06更新
|
748次组卷
|
15卷引用:数学(天津卷)
(已下线)数学(天津卷)天津市十二区重点学校2023届高三下学期联考(二)考前模拟数学试题(已下线)第93练 计算速度训练13天津市北师大静海附属学校2024届高三上学期第三次月考数学试题(已下线)第一次月考卷02-《重难点题型·高分突破》(人教A版2019必修第二册)江苏省常州市联盟学校2022-2023学年高一下学期3月学情调研数学试题云南省昆明市官渡区云南大学附属中学星耀学校2022-2023年高一下学期期中考试数学试题江西省宜丰中学创新部2023-2024学年高一上学期第一次(10月)月考数学试题山东省菏泽市鄄城县第一中学2023-2024学年高一下学期3月月考数学试题江苏省南京市河西外国语学校2023-2024学年高一下学期3月月考数学试卷重庆市杨家坪中学2023-2024学年高一下学期3月月考数学试卷重庆市松树桥中学校2023-2024学年高一下学期第一次段考数学试题黑龙江省牡丹江市第二高级中学2023-2024学年高一下学期4月月考数学试卷广东省江门市第一中学2023-2024学年高一下学期第一次阶段考试数学试题(已下线)模块四期中重组篇云南(高一下人教B版)
10 . 在
中,
,
,
.若
,
分别为边
,
上的点,且满足
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/f73ba7fd5c3f0fbfb7325dbc1e1c1879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ed26db96d51c8157bd5583720cd01a.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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