名校
解题方法
1 . 定义
是向量
和
的“向量积”,其长度为
,其中
为向量
和
的夹角.若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c154a423966d54ab5b08342775c65b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f4f8805346f9d9171c4b62d4110406.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/96044c68866954aa2a84b8d002a86123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/19702ae2c72308f9973ae4c77a62a72e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/127dfac893abd9e5455a561ef6134a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c154a423966d54ab5b08342775c65b.png)
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|
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3卷引用:重庆市育才中学校2022-2023学年高一下学期期中数学试题
2 . 对于向量
,若
,
,
三数互不相等,令向量
,其中
,
,
,
.
(1)当
时,试写出向量
;
(2)证明:对于任意的
,向量
中的三个数
,
,
至多有一个为0;
(3)若
,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681bacf0944746afc82249f50ffb9000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08320e6e96f872f1fcf6ad8096ebaa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7accba7c6d73b12592f0874c69339d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843ff24183004a105ff0c73a1fac6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe08794bdcc386a700cf75d9bb0a255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7455cd15ac74993fb312181398b4695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f7f0bf96b369de82471d9f6b6821b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f8c1951e1335981548165f738e6d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5dba77896ed93d7c27df9d0b2c2154.png)
(2)证明:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61fbe58f038432c468241d2771fb85d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f4ddebf0e34a5c3e9232ae66709aa.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3d50b452aca40b6e77c2a37ff5bac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8ae325b1927be368df207ed6051707.png)
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|
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|
3卷引用:北京市第二十中学2022-2023学年高一下学期3月月考数学试题
名校
解题方法
3 . 设复平面中向量
对应的复数为
,给定某个非零实数
,称向量
为
的
向量.
(1)已知
,求
;
(2)设
的
向量分别为
,已知
,求
的坐标(结果用
表示);
(3)若对于满足
的所有
能取到的最小值为8,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1dbb4c7999d45d14b499e433a09137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fde64d21aa8cf8bd96410f7a0b35a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8626ed40ac561244d7a7d78fdb24bc.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7d9f40ce4648c9729f49cc071fe631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ba4991da3131c3e0cc5126359338e3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aee9563b393021b8a23fd706969828b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8626ed40ac561244d7a7d78fdb24bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff17456ebb5651fe67e874c9b438c17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfb4014c775cf008fadabc87c95866b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95763e154888a080b3b96ff7fb3b39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(3)若对于满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a158c72b071561459803ae1b950d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7c9593bf5727941ac14317c5e730e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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|
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|
3卷引用:上海市七宝中学2021-2022学年高一下学期5月月考数学试题
4 . 已知向量
,其中
,
,
是两两不相等的正整数.记
,
,其分量之间满足递推关系
,
,
,
.
(1)当
时,直接写出向量
;
(2)证明:不存在
,使得
中
;
(3)证明:存在
,当
时,向量
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3690edfe8204c4a6776c18acc206bad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a5771f2c592b64f54f35ba1e2df0dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4573696c9d436bad5052f796d273300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cfe99a43e763e8b7616dadf5d2b7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081925c84c6e1353901510464d3ce395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03365d0f313dce7f007806516611c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0147fb842f714d5c1fe11cc40eedb291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e381c79035a408fccf920a3ca03a9424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee88e2b5d6134e86a66002b99f108da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56425280dbabc756415721e0fa948d35.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e2ccac7a4024918a0c8403118c1d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ec7398767db50242be5776465d5eca.png)
(2)证明:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ab26f71b50d8026097b91b61a5ea67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081925c84c6e1353901510464d3ce395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a4c3e49f8199ba0887b676a0526c59.png)
(3)证明:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7396c9be8cae1ea179e417eb9f5d1377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac60c43c0643492b502a13b68a66e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081925c84c6e1353901510464d3ce395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff887176bb5127935388fd813bc77ab5.png)
您最近一年使用:0次
名校
解题方法
5 . 设向量
与
的夹角为
,定义
,已知
,
,则
( )
![](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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852e6c5d9e1caae5a4b1d12aef8ded06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a99de24f1bdd9dbd91327a25c54f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16ea62296a33638ecd01cebab3b2426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ca3074f563cc1d90ad57c95ff2cdb4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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|
400次组卷
|
2卷引用:黑龙江省哈尔滨市第九中学校2023-2024学年高一下学期6月月考数学试题
6 . 设
、
、
是平面上任意三点,定义向量的运算:
,其中
由向量
以点
为旋转中心逆时针旋转直角得到(若
为零向量,规定
也是零向量).对平面向量
、
、
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/06d77a2cb39a96305fddce29783e4e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709251ddf9c543904f4782247c2cc776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709251ddf9c543904f4782247c2cc776.png)
![](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)
A.![]() |
B.对任意![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.![]() |
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7卷引用:2022年浙江省温州市摇篮杯高一数学竞赛试题
2022年浙江省温州市摇篮杯高一数学竞赛试题重庆市第一中学校2022-2023学年高一下学期4月月考数学试题湖北省武汉市华中师范大学第一附属中学2022-2023学年高一下学期5月月考数学试题(已下线)期中模拟预测卷03(测试范围:必修二前三章)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)(已下线)重难点01平面向量的实际应用与新定义(3)云南省保山市腾冲市第八中学2022-2023学年高一下学期第三次月考数学试题重庆市南开中学校2023-2024学年高一下学期3月阶段测试数学试题
名校
7 . 设O为坐标原点,定义非零向量
的“相伴函数”为
,向量
称为函数
的“相伴向量”.
(1)设函数
,求
的“相伴向量”;
(2)记
的“相伴函数”为
,若函数
,
与直线
有且仅有四个不同的交点,求实数k的取值范围;
(3)已知点
满足
,向量
的“相伴函数”
在
处取得最大值.当点M运动时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2a70e42d715fcd501f6b864c20605f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95a5f3ef304ee910dc162c999672c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e936e203fb157e941e926a8cf8a71980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b4193e142dc3c2a9645ecef60fbe2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37440b57fe2ffc13f2a873e38f55d29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0bac149e19b3a4239cc2355c46f73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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8卷引用:辽宁省大连市第二十四中学2021-2022学年高一下学期期中考试数学试题
辽宁省大连市第二十四中学2021-2022学年高一下学期期中考试数学试题江苏省苏州震泽中学2023-2024学年高一下学期3月月考数学试题江苏省启东中学2023-2024学年高一下学期第一次月考数学试卷湖南省邵阳市第二中学2023-2024学年高一下学期第一次月考数学试题(已下线)模块四 期中重组卷2(江苏南通)(苏教版)山西省阳泉市第一中学校2023-2024学年高一下学期5月期中考试数学试题(已下线)专题13三角恒等变换-2022年新高三数学暑假自学课精讲精练(已下线)专题06 三角函数(讲义)-2
名校
8 . 定义平面向量的一种运算“
”如下:对任意的两个向量
,
,令
,下面说法一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9fc9ca37bc930c9ae9a37a72641747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71d65c9be1d0dc8c8e559494aaf34b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37848d533868519b0938c460d1cb6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76260a0446b2f04cb497a7b4d82d6b61.png)
A.对任意的![]() ![]() |
B.存在唯一确定的向量![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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11卷引用:广东省广州市华南师范大学附属中学2021-2022学年高一下学期期末数学试题
广东省广州市华南师范大学附属中学2021-2022学年高一下学期期末数学试题(已下线)重难点01平面向量的实际应用与新定义(3)专题02平面向量基本定理与平面向量的坐标表示单元测试B卷——第六章 平面向量及其应用山东省潍坊市2022届高三下学期三模统考(5月)数学试题(已下线)专题15平面向量-2022年新高三数学暑假自学课精讲精练(已下线)专题2 “信息迁移”类型(已下线)模块四 三角函数、平面向量与解三角形-3(已下线)第一篇 代数与近世代数 专题2 群、环、域等新定义问题 微点2 群、环、域等新定义问题综合训练加习题(已下线)平面向量及其运算(已下线)压轴题06向量、复数压轴题16题型汇总-1
名校
解题方法
9 . 定义向量
的“伴随函数”为
;函数
的“伴随向量”为
.
(1)写出向量
的“伴随函数”
,并直接写出
的最大值
;
(2)求函数
的“伴随向量”
的坐标;
(3)已知
,向量
、
的“伴随函数”分别为
、
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffa8a04c3f3d20b6bd99c157a33b214.png)
,且
的“伴随函数”为
,其最大值为
.求证:向量
的充要条件为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9354f8346e9004bd73ae7cbbb6f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c6f29b2b1955715616003d51d8b77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c6f29b2b1955715616003d51d8b77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9354f8346e9004bd73ae7cbbb6f52.png)
(1)写出向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2159dcd5f4b6392b9996f09fdbf0b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b897300cdb9af626f62530c285ca3a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae84220aaed30749054f9a2192bec05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffa8a04c3f3d20b6bd99c157a33b214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b320e8296daa8a992a236766aa8f1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed38da21f937df5020532cc9dd35292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224cd491a4b179e1e17f5b1afd85040a.png)
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名校
解题方法
10 . 已知O为坐标原点,对于函数
,称向量
为函数
的相伴特征向量,同时称函数
为向量
的相伴函数.
(1)若
为
的相伴特征向量,求实数m的值;
(2)记向量
的相伴函数为
,求当
且
时
的值;
(3)已知
,
,
为(1)中函数,
,请问在
的图象上是否存在一点P,使得
,若存在,求出P点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c6f29b2b1955715616003d51d8b77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9354f8346e9004bd73ae7cbbb6f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437924f88528ab2bb50866d9fcb5777a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e1c3626b3b44b65712f21480c25dcc.png)
(2)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccbf0d6653c7534dd0ff0ed3cf9e9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2314796f9fd52c819d357fa585327b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54df369856047a0133a25084ec4285d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acf45a5f66394502b70bf1dd68ee40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34458dd7ae8cae1e4a4fd7dd52234032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf88a901d1c39cf022895eec9786f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1428037efcc8068ecc8b4cd2279568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b354aefbabbc26c70388d76919dad557.png)
您最近一年使用:0次
2022-05-04更新
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1404次组卷
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