解题方法
1 . 平面内一组基底
及任一向量
,若点
在直线
上或在平行于
的直线上,我们把直线
以及与直线
平行的直线称为“等和线”,此时
为定值,请证明该结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1625e24072a8fe6c277ecfca2c62cdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923e87f3840ad286b805f2b99ce6e003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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解题方法
2 . 如图,在平行四边形ABCD中,点E是对角线AC上靠近C的三等分点,点F是CD的中点,设
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/12/97a500e7-2f13-4b04-8fed-2becf39714c6.png?resizew=181)
(1)试用
,
分别表示
与
;
(2)利用向量法证明:B,E,F三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/12/97a500e7-2f13-4b04-8fed-2becf39714c6.png?resizew=181)
(1)试用
![](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/84b8a2a41a8b50e10d68943e3f0f4e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75fc81977aee721525b4c5625f5a097.png)
(2)利用向量法证明:B,E,F三点共线.
您最近一年使用:0次
2022-09-11更新
|
574次组卷
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2卷引用:江西省省重点校联盟2022-2023学年高二上学期入学摸底联考数学试题
名校
解题方法
3 . 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
|
712次组卷
|
12卷引用:上海市第二中学2019-2020学年高二上学期期中数学试题
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
名校
解题方法
4 . 已知椭圆
的离心率为
,且椭圆C经过点
.
(Ⅰ)求椭圆C的方程;
(Ⅱ)已知过点
的直线l与椭圆C交于不同的两点A,B,与直线
交于点Q,设
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981fe6f202c7a549a96230f49c11ab89.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f2d7479433c7111ed66a7858b99139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b82fbc73eca81f78c35087c9a6166cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2020-11-06更新
|
1500次组卷
|
7卷引用:山东省临沂市第十九中学2022-2023学年高二上学期期末数学试题
山东省临沂市第十九中学2022-2023学年高二上学期期末数学试题北京市北京师范大学附属中学2022-2023学年高二下学期期中考试数学试题北京高二专题01平面解析几何北京市朝阳区2020届高三年级下学期二模数学试题(已下线)第九单元 解析几何(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷(已下线)专题29 圆锥曲线求定值七种类型大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)北京市第十四中学2023届高三上学期期中检测数学试题
名校
5 . 在平面上,给定非零向量
,对任意向量
,定义
.
(1)若
=(-1,3),
=(2,3),求
;
(2)若
=(2,1),位置向量
的终点在直线x+y+1=0上,求位置向量
终点轨迹方程;
(3)对任意两个向量
,求证∶
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9181079d14f7c1bc9b5b2624f94edca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(3)对任意两个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1721476f7850842ba3dc3d8be33c3723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835ebae7895448fd3d6551b953565ab3.png)
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名校
6 . 已知点
,
,
,其中
,
为实数:
(1)若点
在第二或第三象限,且
,求
的取值范围;
(2)求证:当
时,不论
为何值,
,
,
三点共线;
(3)若
,
,且三角形
的面积为12,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567fc6dde8cea2eccafe83048ed9b650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e33b8cdc93f58e732a696d6a00c7c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af733c6432ce382a8a3fc19ef315ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7506cd409fc15693d2fa0f69fcc0464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.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/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e37a63ee29fda9396419f2eb9a6a6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c747e93ed8de8ad9b477e9c08c84441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
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2019-12-09更新
|
249次组卷
|
2卷引用:上海市南汇中学2018-2019学年高二上学期期中数学试题
7 . 若平面上三点的坐标分别为
,
,
.
(1)用向量法证明:
、
、
三点共线;
(2)设
是坐标原点,且四边形
是平行四边形,求顶点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afee0da488f6cb5f94d949ea26ac7eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36212a7a753aa33a521f0fc27972a9a6.png)
(1)用向量法证明:
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341d9ce62bb00c654b206b35f329740b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2019-11-10更新
|
187次组卷
|
3卷引用:沪教版 高二年级第一学期 领航者 第八章 8.1 向量的坐标表示及其运算(1)
名校
8 . 已知直线l上两个点
,其中O为坐标原点.
(1)若
,求点D的坐标,并确定点D与直线l的位置关系;
(2)已知点B是直线l上的一点,求证:若存在实数m、n,使向量
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a3250dea0fa8753c120925354e2c0e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19c5029ec8d2b180e61c9235cf23a32.png)
(2)已知点B是直线l上的一点,求证:若存在实数m、n,使向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453fb4c9bbc0d4403ff14f7a5d75e0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f371d431b6c91972b742c426c8a81ef.png)
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9 . 已知平行四边形
中,若
是该平面上任意一点,则满足
(
).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e37bff09-0338-46ea-9759-17c509c118ee.png?resizew=194)
(1)若
是
的中点,求
的值;
(2)若
、
、
三点共线,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8f76a25cff46e6dce21b266a3363b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa72c594ebe33496fa7b9edf1db5c7e1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e37bff09-0338-46ea-9759-17c509c118ee.png?resizew=194)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(2)若
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
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10 . 定义:对于两个非零向量
和
,如果存在不全为零的常数
、
,使
,那么称
和
是线性相关的,否则称
和
是线性无关的.已知
,
,试判断
与
的线性关系(相关还是无关),并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647f6682e4de215dce541a013c334a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd379c624402d9206303afb1fd8b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ca94e7c25b02aefacbcb095daa2f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
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