名校
1 . 如图,在梯形
中,
,
,
,
,
在线段
上.
,用向量
,
表示
,
;
(2)若AE与BD交于点F,
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.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/4148817c0a463417ec02769a7abc5913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34bf00aeba15bce2cdee8ab487388dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
(2)若AE与BD交于点F,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eb6b6ee8c74422693cc91262d54070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f673c9b0ad6537149f4d9b3b6d8c63c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7062eabb42603c793fef3a792a9191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-05-23更新
|
376次组卷
|
3卷引用:湖南省岳阳县第一中学、汨罗市第一中学2023-2024学年高一下学期五月联考数学试题
名校
2 . 设
是线段
的中点,
是直线
外一点.
为线段
上的两点,
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e7cd59151397d14cffe4c191c5e380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47182836f477d710442499d08d100f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a733c4da39521e6684636342bb4919ae.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . (1)如图,
,
不共线,
是直线
上的动点,证明:存在实数
,
,使得
,并且
.
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965894555860992/2967921927028736/STEM/1cb3760a-d6bf-42c6-8e0c-e520bd49157b.png?resizew=144)
(2)用向量法证明下列结论:三角形的三条中线交于一点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b0ab2519d0fb666743993961daee47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86ae785512262461ee99e1a724f4f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965894555860992/2967921927028736/STEM/1cb3760a-d6bf-42c6-8e0c-e520bd49157b.png?resizew=144)
(2)用向量法证明下列结论:三角形的三条中线交于一点.
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4 . 如图,正四面体ABCD的棱长为1,E,F分别是棱BD,CD上的点,且
,
,则( )
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927642512080896/2929071801384960/STEM/750527cc-9169-48dd-82f5-fb57f5163294.png?resizew=184)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcdcff2531e0cfca0dafbf5c259b0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da2ab1f8b5d3281efb94b763fa74081.png)
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927642512080896/2929071801384960/STEM/750527cc-9169-48dd-82f5-fb57f5163294.png?resizew=184)
A.直线AC与直线EF异面 | B.存在t,使得![]() |
C.存在t,使得平面![]() | D.三棱锥![]() ![]() |
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2022-03-04更新
|
618次组卷
|
3卷引用:湖南省岳阳市平江县颐华高级中学2023-2024学年高三上学期入学考试数学试题
湖南省岳阳市平江县颐华高级中学2023-2024学年高三上学期入学考试数学试题2022年高三数学新高考测评卷(猜题卷一)(已下线)思想03 数形结合思想(练)--第三篇 思想方法篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》
21-22高一·湖南·课后作业
解题方法
5 . 用向量运算刻画三角形的重心.
(1)已知
,求一点G满足
.
(2)求证:满足条件
的点G是
的重心.
(提示:说明点G同时在
的三条中线上.)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
(2)求证:满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(提示:说明点G同时在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-02-22更新
|
832次组卷
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7卷引用:1.3 向量的数乘
(已下线)1.3 向量的数乘(已下线)专题02 平面向量的运算-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)6.2.3向量的数乘运算(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)6.2.3向量的数乘运算(精练)-【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)湘教版(2019)必修第二册课本习题 习题1.3(已下线)第02讲 平面向量的运算-【寒假预科讲义】(人教A版2019必修第一册)(已下线)专题03 向量的数乘(2)-《重难点题型·高分突破》(苏教版2019必修第二册)
21-22高一·湖南·课后作业
6 . 已知
,设
,
.
(1)求作:
,
,
,
.
(2)向量
,
分别与
有什么关系?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febcf1295fc9f93c64876b128b1d3ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46f9d7ad03ddb15f34255ca71a5445f.png)
(1)求作:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4638caa3bff8208bb05f88db915c09a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d4c53ef927b99fa3f5a2d73b9253a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09174182dab2126107c727b3cc7e601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33935f6c187b9b50ca021795cae0b193.png)
(2)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa37fb49ccaf9821b25852daab11873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f8b77a3b403ea48377e9a3e6e021d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d792a2aa25763e14cc2863be3887000.png)
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21-22高一·湖南·课后作业
7 . (1)如图,O为
的外心,H为
内一点,且
.求证:H是
的垂心,(提示:
.)
所在平面内任一点,其余条件不变,(1)中的结论还成立吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef5de81202c50e6a5f52b955af24722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22eeb58f99ef6398386dcde4a3c3d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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