名校
1 . 如图,平行四边形ABCD中,
.
![](https://img.xkw.com/dksih/QBM/2022/3/29/2946577665048576/2948635542429696/STEM/003c8521-a03f-4968-a374-e5ebccebb23e.png?resizew=187)
(1)若
,E为AM中点,求证:点D,E,N共线;
(2)若
,求
的最小值,以及此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d58684e59bd0cbf2d59589fcd5baa9.png)
![](https://img.xkw.com/dksih/QBM/2022/3/29/2946577665048576/2948635542429696/STEM/003c8521-a03f-4968-a374-e5ebccebb23e.png?resizew=187)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ef664c0aedbd692693ea4a376fa9f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30657d2a85e16c8f38f97e45ab1ac5ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c995e7d79ebfc21814113ae1b15c8569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c7127e3ffa52e588c100d8e6c70f40.png)
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2022-04-01更新
|
1019次组卷
|
5卷引用:山西省运城市2021-2022学年高一下学期3月阶段性检测数学(A)试题
名校
2 . 已知平行四边形ABCD,
,AD⊥BD,E、F分别为AC上2个三等分点.
=
,
=
,|
|=1.,判断DE、BF的位置关系并用向量方法加以证明,求
的值
(2)已知A(1,1),B(5,1),求D点坐标及
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5ae3525aa482c821f7c2402cdb0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa5e480dbb1503156d66b30f0e4e4e9.png)
(2)已知A(1,1),B(5,1),求D点坐标及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5042ed4b58d540d0120f8019f29f3f.png)
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2022-04-06更新
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346次组卷
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4卷引用:湖南省衡阳市田家炳实验中学2021-2022学年高一下学期3月月考数学试题
湖南省衡阳市田家炳实验中学2021-2022学年高一下学期3月月考数学试题山东省莱西市第一中学2022-2023学年高一下学期第一次月考数学试题(已下线)高一数学下学期第一次月考模拟试卷(三角函数+平面向量+解三角形)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)江苏省启东中学2023-2024学年高一下学期第一次月考数学试卷
名校
3 . 如图,在长方形
中,E为边
的中点,F为边
上一点,且
.设
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/18/2938674037768192/2940499691495424/STEM/aa9a17055f144feea5a7b0c8f154ad8e.png?resizew=189)
(1)试用基底
表示
,
;
(2)若
,求证:E,G,F三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571662e11cff4b9a48a3cdf8704977d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b536ac375a0b74e9c7efbc585f987f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4abd10ab43ce90743bd0f79b1f5bfc.png)
![](https://img.xkw.com/dksih/QBM/2022/3/18/2938674037768192/2940499691495424/STEM/aa9a17055f144feea5a7b0c8f154ad8e.png?resizew=189)
(1)试用基底
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e22c0e0b78ae0ce1a0fb6ca107f6658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2173a791f504749b01c97b951be4b940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1307cc4692a34308f7e534e56882b76f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e56a5768de5478030b88d058a841ad.png)
您最近一年使用:0次
2022-03-20更新
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2卷引用:重庆市第八中学2021-2022学年高一下学期第一次月考数学试题
4 . 数学探究:用向量法研究三角形的性质,向量集数与形于一身,每一种向量运算都有相应的几何意义,向量运算与几何图形性质的这种内在联系,是我们自然地想到:利用向量运算研究几何图形的性质,是否会更加方便,简捷呢?请求解下列问题:
![](https://img.xkw.com/dksih/QBM/2022/7/5/3015965509181440/3018355544580096/STEM/fe75f3e15f014f88a1a932d8e6a0997d.png?resizew=165)
(1)用向量方法证明:
三条中线
交于一
点(称为三角形的重心)
(2)设
三顶点
的坐标分别为
求重心的坐标
.
![](https://img.xkw.com/dksih/QBM/2022/7/5/3015965509181440/3018355544580096/STEM/fe75f3e15f014f88a1a932d8e6a0997d.png?resizew=165)
(1)用向量方法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c42f73b6b4cd5308071e6bedb83049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38faf3faf38b331695d509b5f9c24cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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2022-07-08更新
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|
5卷引用:广东省东莞松山湖未来学校2022-2023学年高一下学期3月月考数学试题
广东省东莞松山湖未来学校2022-2023学年高一下学期3月月考数学试题广东省中山市2021-2022学年高一下学期期末数学试题(已下线)6.3.2 -3平面向量的正交分解及平面向量加、减运算的坐标表示(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)期末专题04 平面向量大题综合-【备战期末必刷真题】(已下线)6.3.3平面向量加、减运算的坐标表示(分层作业)-【上好课】
名校
解题方法
5 . 在等边
中,
,点
为
的中点,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/d141659d-41dd-430f-a31f-ff9835dde0b9.png?resizew=168)
(1)证明:点
为
的中点;
(2)若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdf26292f2316f135fdd07a8269ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/d141659d-41dd-430f-a31f-ff9835dde0b9.png?resizew=168)
(1)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f9bab750237301bd7cc234ceb9f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2021-10-10更新
|
820次组卷
|
4卷引用:青桐鸣2022届高三上学期10月大联考数学(理科)试题
青桐鸣2022届高三上学期10月大联考数学(理科)试题广东省广州市二中2021-2022学年高一下学期第一次月考数学试题河南省濮阳市南乐县第一高级中学2022-2023学年高三上学期9月月考理科数学试题(已下线)考点22 平面向量在平面几何、物理中的应用-备战2022年高考数学典型试题解读与变式
名校
解题方法
6 . 在
中,
,点Q为
的中点,
交
于点N.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/e1fd54f6-81e5-4f6d-ae1e-a8985d9dd866.png?resizew=142)
(1)证明:点N为
的中点;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdf26292f2316f135fdd07a8269ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/e1fd54f6-81e5-4f6d-ae1e-a8985d9dd866.png?resizew=142)
(1)证明:点N为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f9bab750237301bd7cc234ceb9f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c923e84cab4d841a72b15993cf8a2a.png)
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解题方法
7 . 设两个非零向量
与
不共线.
(1)若
,
,
,求证:
,
,
三点共线;
(2)向量
与
的夹角
,且
,
,求
与
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fabf836a5eb2105f5a32160b75640c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3919c74b50641196033aa756ac2dd3d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d8fbf3fb296a64537058cced36e1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)向量
![](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/dd15ead753cf2927f51d07c7727c6cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9936a46cc891744d4600f76bb92b694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082c6926889f84f438ea35f70bf05f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
您最近一年使用:0次
2021-08-12更新
|
228次组卷
|
2卷引用:贵州省贵阳清镇北大培文学校2022-2023学年高一下学期3月月考数学试题
名校
解题方法
8 . 如图,在边长为1的正△ABC中,E,F分别是边AB,AC上的点,若
=m
,
=n
,m,n∈(0,1).设EF的中点为M,BC的中点为N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3421342d-9d53-41b5-a727-590904a9afb4.png?resizew=186)
(1)若A,M,N三点共线,求证:m=n;
(2)若m+n=1,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd0cecf5c102254b9755e42a80c3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b8a2a41a8b50e10d68943e3f0f4e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3421342d-9d53-41b5-a727-590904a9afb4.png?resizew=186)
(1)若A,M,N三点共线,求证:m=n;
(2)若m+n=1,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfe64604ee828d439929c94c205c51c.png)
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2021-10-20更新
|
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12卷引用:江苏省苏州市三中2020-2021学年高一下学期3月月考数学试题
江苏省苏州市三中2020-2021学年高一下学期3月月考数学试题山东省滨州市博兴县第二中学2022-2023学年高一下学期第二次月考数学试题四川省凉山州民族中学2023-2024学年高一下学期3月月考数学试题上海市第二中学2019-2020学年高二上学期期中数学试题四川省眉山市彭山区第一中学2019-2020学年高一下学期期中考试数学试题(已下线)专题6.4 平面向量的应用--几何、物理(B卷提升篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版,浙江专用)江苏省镇江市第一中学2020-2021学年高一下学期期中数学试题山东省枣庄市薛城区2020-2021学年高一下学期期中考试数学试题山东省枣庄市第八中学2020-2021学年高一下学期期中考试数学试题(已下线)8.1 向量的概念和线性运算(作业)-【上好课】2020-2021学年高一数学下册同步备课系列(沪教版2020必修第二册)山东省济宁市兖州区2021-2022学年高一下学期期中数学试题沪教版(2020) 一轮复习 堂堂清 第六单元 6.2 向量的分解定理
9 . 已知
、
为椭圆
和双曲线
的公共顶点,
,
分别为双曲线和椭圆上不同于
、
的动点,且满足
(
,
),设直线
、
、
、
的斜率分别为
、
、
、
.
(1)求证:点
、
、
三点共线;
(2)当
,
时,若点
、
都在第一象限,且直线
的斜率为
,求
的面积
;
(3)若
、
分别为椭圆和双曲线的右焦点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb8a277ce3167b75967e7d395f43d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0174a3b3084bea2c770aebceac8b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307e11f7e6896e32aa510bbed949ac6.png)
(1)求证:点
![](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/1dde8112e8eb968fd042418dd632759e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967fdfefb8824635d3fa29daa5396c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4f89cd6b110c525e724e1a872dc18c.png)
您最近一年使用:0次
2021-08-24更新
|
307次组卷
|
3卷引用:江苏省常州市前黄高级中学2021届高三下学期学情检测(二)数学试题
名校
10 . 在平面直角坐标系中,
为坐标原点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7024cce1d5c725910f6ba2e08bf6c8.png)
其中
.
(1)求证:
三点共线;
(2)若函数
的最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7024cce1d5c725910f6ba2e08bf6c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628ca75d4be0305453035fa613704921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771ca8cf4b1c1d8de5ecd33555e4370e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debd3b179cd3a1165bce25f3c48e4595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e75c9db745dc00e734a1ef487bd368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-07-23更新
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174次组卷
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2卷引用:贵州省黔西南州金成实验学校2021-2022学年高一下学期4月质量监测数学试题