名校
解题方法
1 . 设
,
是不共线的两个非零向量.
(1)若
,
,
,求证:
,
,
三点共线;
(2)若
,
,
,且
,
,
三点共线,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d5c5bbd19feecaa7d227949d197c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247578d4a4fc23400b181864ad5f7c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2dfd31a3fd835dd07e05987f0c95d4.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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea4939931d004b13221ecd6f38fb81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f6dec4b2913d8feca73a175a54449f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91575b7543c4c81997356142d67e518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-04-21更新
|
1196次组卷
|
4卷引用:湖北省部分重点中学2022-2023学年高一下学期期中联考数学试题
湖北省部分重点中学2022-2023学年高一下学期期中联考数学试题(已下线)6.2.3向量的数乘运算【第一练】“上好三节课,做好三套题“高中数学素养晋级之路广东省深圳市桃源居中澳实验学校2023-2024学年高一下学期3月全国港澳台侨联考数学试卷专题03平面向量(第三部分)
名校
解题方法
2 . 平行四边形
中,点M在
上,且
,点N在
上,且
,记
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44a918c7cfd942d3a53e584c26685a8.png)
(1)以
,
为基底表示
;
(2)求证:M、N、C三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b661c79b7b866204fd4084c37bdd4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c732356550f7b240d24384bd565c841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac265febbf99dccf51aa0a2253e61f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44a918c7cfd942d3a53e584c26685a8.png)
(1)以
![](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/4dd4b9ad667f6da79bc3a5737cbc1eee.png)
(2)求证:M、N、C三点共线.
您最近一年使用:0次
2022-05-31更新
|
292次组卷
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3卷引用:湖北省云学新高考联盟学校2021-2022学年高一下学期5月联考数学试题
湖北省云学新高考联盟学校2021-2022学年高一下学期5月联考数学试题(已下线)6.3.2&6.3.3&6.3.4 平面向量的正交分解及坐标表示、平面向量加减法运算的坐标表示、平面向量的数乘运算及坐标表示(精讲)(2)-【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)河南省南阳市邓州市第一高级中学校2023-2024学年高一下学期3月月考数学试题
名校
解题方法
3 . 最早对勾股定理进行证明的是三国时期吴国的数学家赵爽,赵爽创制了一幅“勾股圆方图”,他用数形结合的方法,给出了勾股定理的详细证明.如图,某数学探究小组仿照“勾股圆方图”,利用6个全等的三角形和一个小的正六边形ABCDEF,拼成一个大的正六边形GHMNPQ,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f05e7d33737f2e615ba7e94919a1ac.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a19f69f85e053c79a90f03d4319b340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f05e7d33737f2e615ba7e94919a1ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/9921d14d-471e-4e20-8ca9-61a8f34d6fce.png?resizew=145)
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2022-11-18更新
|
650次组卷
|
9卷引用:湖北省襄阳市部分学校2022-2023学年高三上学期期中数学试题
4 . 我们知道,对一个量用两种方法分别计算一次,由结果相同则可以构造等式解决问题,这种思维方法称为“算两次”原理,又称“富比尼原理”,是一种重要的数学思想.例如:如图甲,在
中,D为
的中点,则
,两式相加得
,因为D为
的中点,所以
,于是
.请用“算两次”的方法解决下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0d7c5ade-cae3-4880-8831-e03654f37740.png?resizew=457)
(1)如图乙,在四边形
中,E,F分别为
的中点,证明:
.
(2)如图丙,在四边形
中,E,F分别在边
上,且
,
,
,
,
与
的夹角为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1993fedca8d75454f2c45dd7572319a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15275320d949dd581ec1d51d30443bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08907cc87d17cbe3dfa70f32e91381b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d5ef082556fc084f5f2384b1758683.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0d7c5ade-cae3-4880-8831-e03654f37740.png?resizew=457)
(1)如图乙,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d19f241bd032b79ef71acce794748.png)
(2)如图丙,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940099db7ffe6b3f7e70afcfba66750a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558098da135bc12e7fdca05d14c3848e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ed75e65e7374c38ffb1f75259a8beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fdc83becc28e0f43d71427d9e8775d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89f40b723898ad6c0238faf87d56621.png)
您最近一年使用:0次
名校
5 . 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
|
1378次组卷
|
8卷引用: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
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(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)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
6 . 在平面直角坐标系中,O为坐标原点,A、B、C三点满足
.
求证:A、B、C三点共线;
已知
、
,
,
的最小值为5,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431d15b80cc65e037b35bc10bd8d45e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6611c73064bda197766c00b448dd0030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f8c513fdf6f75cdd4f441e35ecfc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a848eab8a7cd5094a8dc37f9b91f38b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a39a25091e39b138526e12a3937872.png)
您最近一年使用:0次
2018-03-02更新
|
1941次组卷
|
9卷引用:湖北省宜昌市第二中学2018-2019学年高一下学期期中数学试题