名校
1 . 在平行四边形
中,
,
,
. 对角线AC与BD交于点O,E是线段OD的中点,AE的延长线与CD交于点F. 设
,
,则下列结论错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/abc42fcd-0bed-4ccc-8076-119f9618a0c2.png?resizew=220)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f4f259d60ade01bd9bf6632238e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184359fe3cadc363cf4ebe586c2b3db4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/abc42fcd-0bed-4ccc-8076-119f9618a0c2.png?resizew=220)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 在边长为2的正三角形ABC中,D是BC的中点,
,CE交AD于F.①若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
___________ ;②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0192984066d46160038b7623276e2eee.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79b194152945f719c21bbe5d525338d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63451ad70cd68ee791396f6e8eb0132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0192984066d46160038b7623276e2eee.png)
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2022-11-22更新
|
312次组卷
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2卷引用:安徽省合肥世界外国语学校2022-2023学年高一下学期3月阶段性检测数学试题
名校
解题方法
3 . 点P是
所在平面上一点,若
,则
与
的面积之比是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a84ed591e92d2639d6c300a12157fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
A.![]() | B.3 | C.![]() | D.![]() |
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2022-11-14更新
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17卷引用:安徽省六安市六安第二中学河西校区2022-2023学年高一下学期第四次统测数学试题
安徽省六安市六安第二中学河西校区2022-2023学年高一下学期第四次统测数学试题辽宁省沈阳市东北育才学校2022-2023学年高一上学期期中数学试题向量的数乘(已下线)第04讲 平面向量的数乘运算(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)6.3 平面向量基本定理及坐标表示(精讲)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)6.2.3-6.2.4 平面向量的数乘和数量积运算(分层练习)-2022-2023学年高一数学同步精品课堂(人教A版2019必修第二册)(已下线)微专题03 妙用奔驰定理解决三角形面积比问题-【微专题】2022-2023学年高一数学常考点微专题提分精练(人教A版2019必修第二册)(已下线)9.3.1 平面向量基本定理-【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)9.3 向量基本定理及坐标表示(分层练习)-2022-2023学年高一数学同步精品课堂(苏教版2019必修第二册)(已下线)6.3.1 平面向量基本定理(精讲)-【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)内蒙古呼和浩特市土默特中学2022-2023学年高一下学期期中考试数学试题(已下线)期末复习01 平面向量的线性运算-期末专项复习(已下线)6.3.1 平面向量基本定理-高一数学同步精品课堂(人教A版2019必修第二册)(已下线)重难点专题01 妙用奔驰定理解决三角形面积比问题-【帮课堂】(苏教版2019必修第二册)(已下线)专题1.10 奔驰定理及三角形的四心-重难点突破及混淆易错规避(人教A版2019必修第二册)江西省南昌市第五高级中学2023-2024学年高一下学期期中考试数学试卷
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解题方法
4 .
中,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113986d9507fc5015e71989831c128b.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff400c098ae6bf6abd24651a5a21114e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0627c5fbc080e858cea342516ec0f0df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113986d9507fc5015e71989831c128b.png)
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2022-11-12更新
|
684次组卷
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6卷引用:安徽省阜南实验中学2022-2023学年高一下学期4月月考数学试题
安徽省阜南实验中学2022-2023学年高一下学期4月月考数学试题江苏省连云港市灌云高级中学2024届高三上学期11月月考数学试题江苏省盐城市2022-2023学年高三上学期期中数学试题(已下线)6.3.1平面向量基本定理(精讲)(1)-【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)江苏省苏州市2023-2024学年高三上学期11月期中摸底数学试题(已下线)专题04 平面向量(分层练,常考题型+拓展培优+挑战真题)
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解题方法
5 .
中,
,
,
是
外接圆的圆心,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c1671bb42b77ca467df0002940f5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15167b49aad18e17a3b4e58ad6b61c13.png)
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2022-11-09更新
|
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2卷引用:安徽省六安第一中学2022-2023学年高三上学期第三次月考数学试题
名校
6 . 如图,在
中,
,
,P为CD上一点,且满足
,若
,
,则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/4fd814de-3a28-4c17-821b-b6096e761fbd.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d11a5a756d8fdd7b294c4f5fd63467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c9ba21933a3ac9f13936183443e8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da18267294924c440b4a5e1d08dd928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf13d86d78123424a56ef6ccb839bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6897c3746574e32d50ebc92f872cd7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59de90557a43f7a8902463d122e1bfa7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/4fd814de-3a28-4c17-821b-b6096e761fbd.png?resizew=159)
A.![]() | B.![]() | C.1 | D.2 |
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2022-11-09更新
|
1051次组卷
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4卷引用:安徽省六安第一中学2022-2023学年高三上学期第三次月考数学试题
名校
7 . 如图,在平行四边形
中,点
,
分别在
,
边上,且
,
,若
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d19e795e7c26b569a5ec100ac7fcdb8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0192c8bc48647ec635a1720311e18631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6565069f6da2523116c7d7ad2f8fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bfb4b6bbae2e6c93986d136100479d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3ebbff4243c55956aaff429fae282f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ec24953de20381cadbe2e912244728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d19e795e7c26b569a5ec100ac7fcdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/cd1f5e37-2f51-4124-8554-bba08c4f39fa.png?resizew=167)
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2022-10-19更新
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848次组卷
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8卷引用:安徽省皖北县中联盟2022-2023学年高二上学期10月联考数学试题
名校
解题方法
8 . 在
中,
,
为斜边
上一点(不含端点),
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30800bcb030cf5ee97d0e21fbbe8c368.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b803411e826fef958209b3041a605ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30800bcb030cf5ee97d0e21fbbe8c368.png)
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9 . 如图,在三棱锥
中,点G为底面
的重心,点M是线段
上靠近点G的三等分点,过点M的平面分别交棱
,
,
于点D,E,F,若
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d120dea83b3779706b41a32f503f23ce.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757e3a6e3485de706a64977a1612641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fd30e6076e926b4065cb0022d3d99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531541c87dc5fce3a3b1c3a41922ebb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d120dea83b3779706b41a32f503f23ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/009ec3c9-04a6-45f2-a6da-9607962ba46f.png?resizew=167)
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2022-10-12更新
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865次组卷
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8卷引用:安徽省马鞍山市第二十二中学等校2022-2023学年高二上学期阶段联考数学试题
安徽省马鞍山市第二十二中学等校2022-2023学年高二上学期阶段联考数学试题河南省洛阳市强基联盟大联考2022-2023学年高二上学期10月数学试题河北省故城县高级中学2022-2023学年高二上学期第一次月考数学试题江苏省淮安市洪泽湖高级中学2022-2023学年高二下学期第一次月考数学试题辽宁省鞍山市岫岩满族自治县高级中学2022-2023学年高二上学期月考(一)数学试题辽宁省铁岭市昌图县第一高级中学2023-2024学年高二上学期9月月考数学试题江苏省南京市田家炳高级中学2022-2023学年高二下学期期初考试数学试题(已下线)期中押题预测卷(考试范围:选择性必修第一册)(拔高卷)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)
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解题方法
10 . 已知M,P,N是平面上不同的三点,点A是此平面上任意一点,则“M,P,N三点共线”的充要条件是“存在实数
,使得
”.此结论往往称为向量的爪子模型.
(1)给出这个结论的证明;
(2)在
的边
、
上分别取点E、F,使
,
,连结
、
交于点G.设
,
.利用上述结论,求出用
、
表示向量
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba27da4302c066fa4cf802ef5829b90.png)
(1)给出这个结论的证明;
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12936b86da4c79d7705b233baa336ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b80c5888abb4ac33ae0ec9d834a9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d82dcb8d9047d6769989282c53b08e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5691149a894127b6dccf09cb340d4247.png)
![](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/4db1ab520617e340ca2d38b104bd3598.png)
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