名校
1 . 如图,在
中,
,
,
与
相交于点M,设
,
.
![](https://img.xkw.com/dksih/QBM/2023/4/20/3220492268240896/3260429104324608/STEM/883bb566982f4a92abfc627914cc4934.png?resizew=130)
(1)试用向量
,
表示
;
(2)过点M作直线
分别交线段
,
于点E,F,记
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f538d976044e8282916a6da0da4e557e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d24514cfd797f21116cacd6d636df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://img.xkw.com/dksih/QBM/2023/4/20/3220492268240896/3260429104324608/STEM/883bb566982f4a92abfc627914cc4934.png?resizew=130)
(1)试用向量
![](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/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(2)过点M作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c70d3674afde7efd0bbafc68e50b828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bfb6d4191082a234e18ba331fe1ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c227da7ad9d24ae3e3740febf9f293.png)
您最近一年使用:0次
2023-06-15更新
|
330次组卷
|
5卷引用:江苏省泰州中学2017-2018学年高一12月月考数学试题
江苏省泰州中学2017-2018学年高一12月月考数学试题【全国百强校】福建省仙游第一中学2017-2018学年高一下学期第二次月考数学试题(已下线)2017-2018学年下学期期末复习备考之精准复习模拟题高一数学(C卷)(第02期)江西省抚州市七校2022-2023学年高一下学期期中联考数学试题安徽省安庆市怀宁县新安中学2024届高三第二次质检考试数学试题
名校
2 . 已知平面直角坐标系中,点
,点
(其中a,b为常数,且
),点O为坐标原点.如图所示,设点
是线段
的n等分点,其中
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/6cbaf455-8586-4b8a-a69b-b3b8e5d0cf3a.png?resizew=187)
(1)当
时,求
的值(用含a,b的式子表示);
(2)当
时,求
的最小值.
(说明:可能用到的计算公式:
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60eadd52137f72532d91289ff1b02e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b389c7bd3cd4f58a5a271cc4665ad5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/6cbaf455-8586-4b8a-a69b-b3b8e5d0cf3a.png?resizew=187)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3805398b3ea0a1d2e5249877e2a2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc89cb24928b18be5c9c95b5f779ebf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c578add93be18e27b7798a50e5f0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc01794f90fddc5b5b3809995dd7ab1.png)
(说明:可能用到的计算公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5bbc6f6636b605f370483ef8268051.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在
中,已知
为
边上的中点,点
在线段
上,且
;
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942404491608064/2944018805284864/STEM/a970ffe150984b3eb91a99fb26971bb4.png?resizew=331)
(1)求线段
的长度,
(2)设
与
相交于点
,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ad28741a054dd42e39c738045ee80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35378828ca211fae49c9a4efc2d61678.png)
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942404491608064/2944018805284864/STEM/a970ffe150984b3eb91a99fb26971bb4.png?resizew=331)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
您最近一年使用:0次
2022-03-25更新
|
652次组卷
|
6卷引用:江苏省无锡市南菁高级中学2021-2022学年高一下学期第一次阶段考试数学试题
4 . 如图所示,
是边长为2的正三角形,点
,
,
四等分线段BC.
(1)求
的值;
(2)若点Q是线段
上一点,且
,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/26/a19508e5-d8ea-47c4-b8fe-eca20a762f14.png?resizew=160)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f3c6cde5b7ce206cb82be06bed1726.png)
(2)若点Q是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af60dbda52ecc12748d1dab69b156be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafb1230cd6cb30987b5c2a3851f6636.png)
您最近一年使用:0次
解题方法
5 . 如图,在
中,已知
,D为线段
中点,E为线段
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/fac6a310-bee3-485d-be14-c719f7a3db67.png?resizew=159)
(1)求
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc72760a5ded079455e10cb1deafc443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/fac6a310-bee3-485d-be14-c719f7a3db67.png?resizew=159)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12cd088a6f16ee92bb314494426f11c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15554b45e9c66c5fc508d701f00e0f0.png)
您最近一年使用:0次
2021-05-01更新
|
1039次组卷
|
3卷引用:江苏省新区实验2020-2021学年高一下学期期中数学试题
江苏省新区实验2020-2021学年高一下学期期中数学试题(已下线)专题01 平面向量及其应用-2020-2021学年高一数学下学期期末专项复习(苏教版2019必修第二册)四川省成都市新都区2020-2021学年高一下学期期末数学试题
名校
6 . 如图,
三点不共线,
,
,设
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/104627b2-6d7c-4412-8e00-ac13fced4943.png?resizew=214)
(1)试用
表示向量
;
(2)设线段
的中点分别为
,试证明
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5e21d225bf3c159ddf3876fbb8fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4889c71f59b01a0b85203516999172b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31b499b2946ba89853377d59b972b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe136ff8396ff6f80de6e616f290717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cae49aecae12a1aaaa29cb194a11bd3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/104627b2-6d7c-4412-8e00-ac13fced4943.png?resizew=214)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116e2e7116a7b5cd0a912ec0699ca017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d95523797cb4cc9e807180c5648adba.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270b1fa1a61e460581cb408cef8dd3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8eb8ce67d4a46a38bd00b35c1ffced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8eb8ce67d4a46a38bd00b35c1ffced.png)
您最近一年使用:0次
2020-05-09更新
|
1379次组卷
|
8卷引用:9.4 向量应用 2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)
(已下线)9.4 向量应用 2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)湖北省襄阳五中2019-2020学年高一下学期网上学习3月月考数学试题沪教版(2020) 必修第二册 单元训练 第8章 向量的概念和线性运算 (B卷)1.4向量的分解与坐标表示(一)广东省惠珠联考2023-2024学年高二上学期10月联考数学试题(已下线)专题07 向量的应用-【寒假自学课】(苏教版2019)(已下线)第六章 本章综合--归纳本章考点【第一课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)6.4.1 平面几何中的向量方法-同步题型分类归纳讲与练(人教A版2019必修第二册)
名校
7 . 在△ABC中,点D,E,F分别在边AB,BC,AC上,且
,
,
,P是CD,EF的交点.设
,
.
(1)用
,
表示
,
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cadd71e033cdf5d80936ca1cb4398dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdf0a9eef16e289e64e65adaa8e0b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a113dc62db61e60349255fe830db6cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
(1)用
![](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/c3ed9c2e9fabbfc63733bae8fa079d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3134c63f85a55d94233e95198c3e6491.png)
您最近一年使用:0次
2022-04-22更新
|
593次组卷
|
3卷引用:专题05 平面向量基本定理-《重难点题型·高分突破》(苏教版2019必修第二册)
(已下线)专题05 平面向量基本定理-《重难点题型·高分突破》(苏教版2019必修第二册)河南省创新发展联盟2021-2022学年高一下学期联考(三)数学试题重庆市缙云教育联盟2023-2024学年高二上学期9月月度质量检测数学试题
名校
解题方法
8 . 在锐角
中,
,点O为
的外心.
(1)若
,求
的最大值;
(2)若
.
①求证:
;
②求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ea81a4761aa43976c2b9be0b0dd16b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8954ac84d5a64358d2876a62f2a439b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f28d6011934956775d9eae744423fa3.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e61f34f8eb548af6c30bbe8d23a52ae.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a442e21ce6d4de5fd2392ad94f7dace3.png)
您最近一年使用:0次
2024-04-16更新
|
334次组卷
|
7卷引用:江苏省南京市中华中学2022-2023学年高一下学期3月综合练习数学试题
江苏省南京市中华中学2022-2023学年高一下学期3月综合练习数学试题江苏省南京外国语学校2023-2024学年高一下学期5月阶段性测试数学试题福建省厦门第一中学2021-2022学年高一3月月考数学试题(已下线)专题4平面向量综合闯关 (提升版)(已下线)高一数学下学期期中模拟试题02(平面向量、解三角形、复数、立体几何)(已下线)专题6.12 平面向量及其应用全章综合测试卷(提高篇)-举一反三系列福建省厦门市外国语学校2023-2024学年高一下学期第一次月考数学试题
名校
9 . 如图,在矩形
中,点
在边
上,
,且
.M是线段
上一动点.
(1)M是线段
的中点,求
的值;
(2)若
,求
的最小值.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79b194152945f719c21bbe5d525338d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/8c13a780-1b39-44a1-ac37-0e1bec6e7698.png?resizew=173)
(1)M是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267f14afad334ea1ab7f31da18ad94c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee9cc31cc9e01d70778ad5303ca6f34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507a8287b329e51a74b9d7f1b2f290d9.png)
您最近一年使用:0次
10 . 如图所示,在平行四边形
中,点
为
中点,点
在
上,且
,记
,
.
为基底表示
;
(2)求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a0103adccc3223f8d327aadf409207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184359fe3cadc363cf4ebe586c2b3db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a40e1ebf192fda9c0177b4be1870643.png)
您最近一年使用:0次