名校
解题方法
1 . 如图,在
中,
,D为
中点,P为
上一点,且满足
,
的面积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
___________ ;
的最小值为___________ .
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991522285035520/2992033701797888/STEM/f9c92d49-da4e-4b23-a910-6d5ad8c4d1df.png?resizew=190)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d48292e1f9b7fb8b704523b4968096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f73bf2c8f7430a43fc8127e7713e7fc4.png)
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991522285035520/2992033701797888/STEM/f9c92d49-da4e-4b23-a910-6d5ad8c4d1df.png?resizew=190)
您最近一年使用:0次
2022-06-01更新
|
1274次组卷
|
4卷引用:天津市耀华中学2022届高三下学期二模数学试题
天津市耀华中学2022届高三下学期二模数学试题天津市第九十五中学益中学校2022-2023学年高三上学期开学检测数学试题(已下线)10.1 平面向量的线性运算及基本定理(精练)(已下线)拓展一:平面向量的拓展应用 (精讲)(2) - 【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)
解题方法
2 . 已知菱形
的边长为
,
是
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3161dc51156fe680093fe731ba038d8d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3161dc51156fe680093fe731ba038d8d.png)
您最近一年使用:0次
名校
3 . 已知平面四边形
,
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
______ ;动点
,
分别在线段
,
上,且
,
,则
的取值范围为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9633909058247a8aba7d17ae126d825e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.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/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34e6e119b3d828c7246f909ec4e9810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5f7c7dac2d664f3f6b5deed1f95924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7173b357dec0dca7d6da123345089741.png)
您最近一年使用:0次
名校
解题方法
4 . 在等腰梯形
中,已知
,
,
,
,动点E和F分别在线段
和
上,且
,
,当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
__________ 时,则
有最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4aa43d2e64e857267e706e1f50f5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e513fd59e59bda50100de1b4571a235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4c4e86d79aab9d8383e0372c23cf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7173b357dec0dca7d6da123345089741.png)
您最近一年使用:0次
2022-05-27更新
|
1747次组卷
|
7卷引用:天津市南开区2022届高三下学期三模数学试题
天津市南开区2022届高三下学期三模数学试题天津市和平区第二十中学2022-2023学年高三上学期期中数学试题天津外国语大学附属外国语学校2022-2023学年高三上学期期末数学试题(已下线)广东省广州市天河区2023届高三二模数学试题专题11平面向量(已下线)拓展一:平面向量的拓展应用 (精讲)(2) - 【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)江苏省苏州市相城区陆慕高级中学2022-2023学年高一下学期3月月考数学试题
名校
5 . 如图,在菱形ABCD中
,E、F分别为BC、CD上的点.
,点M在线段EF上,且满
,则
___________ ;若点N为线段BD上一动点,则
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78144f8d301153dfe67333609cd9816d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac5a6e955fadd773b2ef8a28e7b2a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8e5ca0fc0f55fc196e00f05230ca06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace429385657ca471ea5d26c85463917.png)
您最近一年使用:0次
2022-05-26更新
|
1074次组卷
|
5卷引用:天津市九校联考2022届高三下学期一模数学试题
天津市九校联考2022届高三下学期一模数学试题天津市第四中学2022-2023学年高三上学期期末数学试题天津市民族中学2024届高三下学期4月校内模拟检测数学试卷(已下线)10.2 平面向量的数量积(精讲)(已下线)6.4.1平面几何中的向量方法+6.4.2向量在物理中的应用举例(精讲)-【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)
名校
6 . 在梯形
中,
与
相交于点Q.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0266627309446d599513540ad73b688.png)
________ ;若
,N为线段
延长线上的动点,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d98befb0f03f2efc324d294a6b4bdb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaed049ce72105d5f10bbc2e80b78aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0266627309446d599513540ad73b688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a00604fc0ba075e219b515428fbd87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b85295316a529d3c1d67cb3853b1ee.png)
您最近一年使用:0次
2022-05-24更新
|
1837次组卷
|
7卷引用:天津市环城七校联考2022届高三下学期第二次质量调查数学试题
天津市环城七校联考2022届高三下学期第二次质量调查数学试题天津市滨海新区塘沽第一中学2022-2023学年高三上学期第一次月考数学试题(已下线)10.2 平面向量的数量积(精练)(已下线)数学(天津B卷)天津市实验中学滨海学校2022-2023学年高一下学期期中数学试题(已下线)第02练 平面向量的数量积-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)第六章 平面向量及其应用 单元复习提升(1)-单元速记·巧练(人教A版2019必修第二册)
解题方法
7 . 已知平行四边形
中,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed97dbde73cd89bfc1abeb3ac7890f2.png)
________ ;若
,
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73eb63d44d1c9dea0a1c0fbd0b4675e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed97dbde73cd89bfc1abeb3ac7890f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb0f7572cae30e297837bcc36b43411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf2b9a8ea7faf6c838e7b14065f6d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eada92a7ad4629e4026d5e1cb1e6f578.png)
您最近一年使用:0次
2022-05-17更新
|
2184次组卷
|
6卷引用:天津市南开区2022届高三下学期二模数学试题
天津市南开区2022届高三下学期二模数学试题天津市北辰区第九十六中学2024届高三上学期12月阶段性检测数学试题天津市北辰区第九十六中学2024届高三上学期第二次月考数学试题(已下线)专题9 平面向量数量积的最值问题(已下线)2023年天津高考数学真题变式题11-15(已下线)拓展一:平面向量的拓展应用 (精讲)(2) - 【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)
名校
解题方法
8 . 在△ABC中,
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a27dc396251a4453094d19baa79816.png)
___________ ,若动点F在线段AC上,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b3132ee4ecd6fa68a8492853b1057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c5d0cd7e9863d353bc40f67aad117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e21c601165e688406b90377c591393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a27dc396251a4453094d19baa79816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de87b1aeaeb7ba1cf3b205eaf441cae.png)
您最近一年使用:0次
2022-05-10更新
|
2020次组卷
|
9卷引用:天津市十二区县重点学校2022届高三下学期毕业班联考(一)数学试题
天津市十二区县重点学校2022届高三下学期毕业班联考(一)数学试题天津市七校联考2022-2023学年高三下学期总复习质量调查(一)数学试题天津市第四中学2023届高三高考热身数学试题天津市实验中学滨海学校2023-2024学年高三上学期第一次质量检测数学试题天津市河西区第四十二中学2024届高三上学期第二次月考数学试题(已下线)2022年高考天津数学高考真题变式题4-6题(已下线)2022年高考天津数学高考真题变式题13-15题(已下线)10.2 平面向量的数量积(精讲)(已下线)6.2.4 向量的数量积 (精讲)(2)-【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)
名校
9 . 如图,在菱形
中,
,
,
、
分别为
、
上的点,
,
,若线段
上存在一点
,使得
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1fca278ad073e7a67642ababf077.png)
____ ;若
,则
的最大值为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acd69f9a7b4f4b7176eba8a2388631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c0f3e6987b64c46a9fddbf1588510b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb064f478d74e6a2af2553206f875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1fca278ad073e7a67642ababf077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05684d6873a8805e13bd454d8070389a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c6eb9d2c645f5eb5bed799b3b8137.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/75b82c47-05c7-4cd3-b437-cf6635da3513.png?resizew=202)
您最近一年使用:0次
2022-05-03更新
|
945次组卷
|
4卷引用:天津市滨海新区塘沽第一中学2022届高三下学期高考适应性测试数学试题
名校
10 . 在矩形ABCD中,
,
,P是对角线AC上一点,
,过点P的直线分别交DA的延长线、DC于M,N,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6843672f1765682d7b4670d1960fdc4.png)
___________ ,若
,
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfea554ca3c2d6d99c1d1ea1ea601697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6843672f1765682d7b4670d1960fdc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6160694d8be9cfa27d0757467eb528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa3a1c721a29edc49bc3cdb308a50fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817a48b819ab971e79bad7b20250294.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966573086343168/2967920796311552/STEM/fbe7df30-a142-4ba4-9a8e-8782d0b4fed0.png?resizew=181)
您最近一年使用:0次
2022-04-28更新
|
1218次组卷
|
2卷引用:天津市河东区2022届高三下学期一模数学试题