名校
解题方法
1 . 如图所示,
中,AQ为边BC的中线,
,
,
,
,其中
,
,
,
.
(1)当
时,用向量
,
表示
;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925a8f79866d00685bde19adb8548a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c270fca58d3736b4786dd92a78858ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6bd78eaf4e6b4a904b9850392fcf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323f0075c96990706da0ba1d81c91ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c98c0ec4c99989333faa478a946985.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/13/63839967-0068-4c19-ad4c-2997f774e4ae.png?resizew=174)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19215074e16c7288e853d336897bead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7038add4e76bba5957f61ff4f85d7b53.png)
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2023-09-13更新
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5卷引用:安徽省皖江名校2023-2024学年高二上学期开学联考数学试题
安徽省皖江名校2023-2024学年高二上学期开学联考数学试题6.3.1平面向量基本定理练习(已下线)专题05 平面向量基本定理-【寒假自学课】(苏教版2019)(已下线)9.3 向量基本定理及坐标表示1-【帮课堂】(苏教版2019必修第二册)(已下线)2.4 平面向量基本定理及坐标表示-同步精品课堂(北师大版2019必修第二册)
2022高一·全国·专题练习
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2 . 设两个非零向量
与
不共线.
(1)若
,求证:
三点共线;
(2)试确定实数
,使
和
反向共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda7620e1edf5a1b05592232bf5472db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65183d238c9bc2be73770717d890683.png)
(2)试确定实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b625b8d3178dd0ea451a80a63082c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9441846da0868582298cece138bec3e.png)
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2023-07-23更新
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9卷引用:安徽省阜南实验中学2022-2023学年高一下学期4月月考数学试题
安徽省阜南实验中学2022-2023学年高一下学期4月月考数学试题(已下线)专题01 有关向量共线的问题 -【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第03讲 向量的数乘(已下线)微专题01 共线问题与数量积求解策略(1)-【微专题】2022-2023学年高一数学常考点微专题提分精练(人教A版2019必修第二册)甘肃省武威市民勤一中、天祝一中、古浪一中2022-2023学年高一下学期第一次月考数学试题(已下线)专题03 平面向量基本定理及坐标表示(六大考点)-【寒假自学课】(人教A版2019)辽宁省本溪市第一中学2023-2024学年高一下学期寒假验收考试数学试题广东省梅州市梅县区丙村中学2023-2024学年高一下学期期中段考试数学试卷山东省菏泽市鄄城县第一中学2023-2024学年高一下学期5月月考数学试题
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3 . 如图,在△ABC中,三内角A,B,C对应的边分别为a,b,c,点E是边AB的中点,点D是边AC上一点,BD,CE相交于点P,且
.
(1)若
,求实数
的值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270b6402b10f97389b63506859cc9744.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/30/d930428c-8ef5-46df-9f7e-65d3d48fb5c2.png?resizew=179)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8187ab01a959abdff6f9da304143f238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e8775a682511e43fd09fa38e4e4d5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72264e1962289ff8cc3caf451b34bab1.png)
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4 . 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)
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5卷引用: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
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
名校
解题方法
5 . 如图,在
中,
,
,
与
相交于点M,设
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/c2602b95-7021-4cf6-9260-7a9cd9d7fc90.png?resizew=207)
(1)试用
,
表示向量
:
(2)在线段
上取一点E,在
上取一点F,使得
过点M,设
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6db75d7769d4866644abb4e46896d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef86ffd2bf72dcfb82b82f839a35e452.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/732e8008564ec12576ac60e498b28067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e42eacb57037d08cf18946fe8e33bc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/c2602b95-7021-4cf6-9260-7a9cd9d7fc90.png?resizew=207)
(1)试用
![](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/9b6799b234237333b0efa331d98f0374.png)
(2)在线段
![](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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9795568e7c599718a29bc80cc3405233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4fdd03782afd69e06cdd75fb050b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede0971558b2fda47c16acab961f31ae.png)
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2021-10-16更新
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12卷引用:安徽省滁州市定远县育才学校2021-2022学年高一下学期期中考试数学试题
安徽省滁州市定远县育才学校2021-2022学年高一下学期期中考试数学试题安徽省滁州市定远县育才学校2021-2022学年高一下学期第一次月考数学试题人教A版(2019) 必修第二册 必杀技 第6章 6.3.1 平面向量基本定理人教B版(2019) 必修第二册 学习帮手 第六章 6.2.1 向量基本定理(已下线)6.3平面向量基本定理及坐标表示C卷山西省大同市第一中学校2021-2022学年高一下学期4月学情检测数学试题苏教版(2019) 必修第二册 过关斩将 第9章 9.3.1 平面向量基本定理(已下线)微专题02 平面向量的基本定理(2)-【微专题】2022-2023学年高一数学常考点微专题提分精练(人教A版2019必修第二册)贵州省黔西南布依族苗族自治州兴义市顶效开发区顶兴学校2022-2023学年高一下学期第一次月考数学试题 第六章平面向量章节检测—2021-2022学年高一上学期数学人教B版(2019)必修第二册(已下线)第五篇 向量与几何 专题12 等和线 微点2 等和线定理及其应用(二)(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)