名校
1 . 如图所示,在四棱锥M﹣ABCD中,底面ABCD是边长为1的正方形,且AM和AB,AD的夹角都是60°
是
的中点,设
,
,
,试以
,
,
为基向量表示出向量
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21841338587f28e2b8adbc39897a145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3bfd659390349bb6dd15bb4ae57260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252b637d25263b74a01ec59e691c3a45.png)
![](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/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350f162ee9aa08f4c9779481a5ef1025.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/b4cee695-ea61-4241-83ef-a10e03f74551.png?resizew=145)
您最近一年使用:0次
名校
2 . 如图所示,在
中,D为BC边上一点,且
.过D点的直线EF与直线AB相交于E点,与直线AC相交于F点(E,F两点不重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/4d3b5000-2fae-47a8-b4d0-0ac2728d5337.png?resizew=184)
(1)用
,
表示
;
(2)若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff400c098ae6bf6abd24651a5a21114e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/4d3b5000-2fae-47a8-b4d0-0ac2728d5337.png?resizew=184)
(1)用
![](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/304a7f07db2ec637baadf8f0ab91c85c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4425dc7c346e4597c0521d7f636174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3605b320cae7b4a85aa273dfb7e606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c227da7ad9d24ae3e3740febf9f293.png)
您最近一年使用:0次
2022-12-30更新
|
2719次组卷
|
19卷引用:辽宁省大连市2022-2023学年高一上学期期末数学试题
辽宁省大连市2022-2023学年高一上学期期末数学试题辽宁省葫芦岛市第一高级中学2023-2024学年高一上学期期末复习数学拓展提升卷(二)(已下线)6.3.1-6.3.3 平面向量基本定理、正交分解及坐标表示、加、减运算的坐标表示2-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)第六章《平面向量及其应用》同步单元必刷卷(培优卷)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)6.3.1 平面向量基本定理(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)9.3.1 平面向量基本定理1河北省高碑店市崇德实验中学2022-2023学年高一下学期2月月考数学试题第九章 平面向量(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)(已下线)第9章:平面向量 重点题型复习-【题型分类归纳】2022-2023学年高一数学同步讲与练(苏教版2019必修第二册)(已下线)专题6.13 平面向量的综合运用大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)第六章:平面向量及其应用 重点题型复习(1)-【题型分类归纳】(已下线)模块三 专题5 大题分类练(平面向量)基础夯实练(北师大版)(已下线)模块三 专题4 大题分类练(平面向量)基础夯实练(人教A)(已下线)模块三 专题4 大题分类练(平面向量)基础夯实练(苏教版)(已下线)期末专题04 平面向量大题综合-【备战期末必刷真题】湖北省荆州市荆州区2022-2023学年高一下学期期中联考数学试题云南省昆明师范专科学校附属中学2022-2023学年高一下学期6月质量监测数学试题河南省南阳市唐河县文峰高级中学2022-2023学年高一下学期期中模拟(一)数学试题江苏省连云港市赣榆第一中学2022-2023学年高一下学期3月月考数学试题
3 . 如图,已知点G是
的重心,点P是
内一点(包括边界),设
,
.
![](https://img.xkw.com/dksih/QBM/2022/7/7/3017651300950016/3025018046504960/STEM/de1cb916dad54c98855229002b66c084.png?resizew=190)
(1)试用
,
表示
,并求
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffffbccf0eb96123a237860c12a1b892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
![](https://img.xkw.com/dksih/QBM/2022/7/7/3017651300950016/3025018046504960/STEM/de1cb916dad54c98855229002b66c084.png?resizew=190)
(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/670f6533aaf27dd575f4f26e0c5928d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0d5fd8f951e3aab842dfd18f2f7f18.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d88fce4e09a7e9acfd154f0b8d42b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
解题方法
4 . 如图,在平行四边形
中,
,
,
,
与
的夹角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/22/41605815-fef7-45da-82be-d6affe74debc.png?resizew=184)
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a8a071a58168a13919329f1466b597.png)
,求
的值;
(2)求
与
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba48db7f17b1a65196715acc7c5b847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ffa9ee27512a2b7115b55b5ff67d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231001e8bf158e295461f3377fd5b728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d1308d5db144e31b4d0211c63ef52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/22/41605815-fef7-45da-82be-d6affe74debc.png?resizew=184)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a8a071a58168a13919329f1466b597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16129a62cce31044b3a3b6eeb3b71c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dbae9556d1b072fbc48b1ac9e2dfde.png)
您最近一年使用:0次
5 . 下图,直线
与
的边
,
分别相交于点
,
.设
,
,
,
,请用向量方法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c884a45b56bc34d79273b067c1520b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd37b64af6bbdbf18adf222b8a5865ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad21f3682a4949e36a2c18fac6a5807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5b98ffb5258ca17bc6705972c97113.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/8/1de75aec-3457-44d9-92cc-046230c7761e.png?resizew=203)
您最近一年使用:0次
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解题方法
6 . 在△ABC中,角A,B,C的对边分别为a,b,c,且
.
(1)求B;
(2)若D为边AC的中点,且
,求中线BD长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ed83082881768d201d971d4d482721.png)
(1)求B;
(2)若D为边AC的中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308fe6faf8a294854a6783ef29cb81b1.png)
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解题方法
7 . 如图,直角三角形
中,
,
,
,D是AB的中点,M是CD上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/c12115fa-fec8-407d-8347-d1965ef247b1.png?resizew=208)
(1)计算
的值;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/30/c12115fa-fec8-407d-8347-d1965ef247b1.png?resizew=208)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6fc69941a8ebdc0d3728da9b220101.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bb7eb64f60555fa24c8feeedd43657.png)
您最近一年使用:0次
8 . 如图,在平行四边形
中,
.
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991301356453888/2995795501948928/STEM/f31bb9b7-fd25-419f-b30e-c51b53b81e3c.png?resizew=228)
(1)用
表示
;
(2)若
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc64dd675992a381ebc4a63a707d4c9.png)
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991301356453888/2995795501948928/STEM/f31bb9b7-fd25-419f-b30e-c51b53b81e3c.png?resizew=228)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd19d458d51304d5b5709003af66e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e6bbd6bea8adff69cd6ee068213836.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c636388d0ddb28ca41364cccfa55a7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32c94eebcd745ffea7b9f3c760e45b4.png)
您最近一年使用:0次
2022-06-07更新
|
441次组卷
|
2卷引用:陕西省商洛市2021-2022学年高一下学期期末数学试题
解题方法
9 . 如图,在四棱锥
中,底面ABCD是边长为1的菱形,且
,侧棱
,
,M是PC的中点,设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e4692921-2976-4e9b-8d88-4aae70efaf9f.png?resizew=165)
(1)试用
,
,
表示向量
;
(2)求BM的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe7dbabffc55ed62994b9145a0f2e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac265febbf99dccf51aa0a2253e61f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44a918c7cfd942d3a53e584c26685a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368d8a829d16a657977dd964df9789e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e4692921-2976-4e9b-8d88-4aae70efaf9f.png?resizew=165)
(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/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4648d56ec5ba86c288bc22737250ba0.png)
(2)求BM的长.
您最近一年使用:0次