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1 . 下列说法正确的是( )
A.在![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() |
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5卷引用:浙江省嘉兴市桐乡市高级中学2022-2023学年高二上学期9月检测数学试题
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解题方法
2 . 我国著名数学家华罗庚曾说过:“数缺形时少直观,形少数时难入微,数形结合百般好,隔离分家万事休”.数学中,数和形是两个最主要的研究对象,它们之间有着十分密切的联系,在一定条件下,数和形之间可以相互转化,相互渗透.而向量正是数与形“沟通的桥梁”.在
中,试解决以下问题:
于点
.
(i)记
,请用
表示
;
(ii)
,求
的最小值.
(2)已知点O是
的________,且
,求
.
请从下面两个条件中选一个填在上述横线上,并完成解答.(注意:如果选择多个条件分别解答,则按第一个解答计分)
①外心(三条垂直平分线的交点);②垂心(三条高的交点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(i)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d759efa8394237b330b99e220e0174e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a838d9d01d18ed8cfb34d302cd74c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f6533aaf27dd575f4f26e0c5928d9.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3d786403d56822ee8b5fea39c0941f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4a7a7b5944c122af3ed4379c2de229.png)
(2)已知点O是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b4eb27553163b22b2799e3e7864261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5cb63aeea0b37799404c8fec092b21d.png)
请从下面两个条件中选一个填在上述横线上,并完成解答.(注意:如果选择多个条件分别解答,则按第一个解答计分)
①外心(三条垂直平分线的交点);②垂心(三条高的交点).
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2022-04-25更新
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6卷引用:山西省山西大学附属中学校2021-2022学年高一下学期4月月考数学试题
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解题方法
3 . 在
中,
.
为
的重心,试用
、
表示
;
(2)如图2,若点
在以
为圆心,
为半径的圆弧
上运动(包含
、
两个端点),且
,设
,求
的取值范围;
(3)如图3,若点
为
外接圆的圆心,设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259414bba09b088ca98ed4c3fcee8197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f654198c1e01d97f1378b35d7c68ca.png)
(2)如图2,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b631cd7917b0ac877f875e26c2b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
(3)如图3,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d04286510bedf469f1a53160b21c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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2021-07-19更新
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6卷引用:上海市奉贤中学2021-2022学年高一下学期5月月考数学试题
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4 . 关于平面向量,下列说法正确的是( )
A.若![]() ![]() ![]() |
B.已知![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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2卷引用:山东省临沂第一中学2021-2022学年高一下学期6月月考数学试题
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解题方法
5 . 在
中,点D在边BC上,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec8bc62f9491231ad5b8527dbd07ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace1f0505dac8a8ea7bca12dc94eb41.png)
,记
中点分别为
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d78524f98b01fa1dadfd277939665b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec8bc62f9491231ad5b8527dbd07ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace1f0505dac8a8ea7bca12dc94eb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158a47ad74fdd9a44e9fc0403d6381b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dab67d1b4a722079cd03b7b0a0e89ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3767efa8adfb71001ad39df9560cbf6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6f1b16c63ef1269d4f5b366e7b3b94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:江苏省南京市、盐城市部分学校2022-2023学年高三上学期10月第一次联合调研数学试题
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解题方法
6 . 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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解题方法
7 . 在平面直角坐标系
中,
是直线
与曲线
在第一象限的交点,
是直线
上的一点,且满足
.
为曲线
上动点,当
取最小值时,
的横坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2fa89a25879322c4cb884763b79104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f415ebe14b7a5b4fbc3f86393d887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7937ef6b4a2b4d25dc8bbd6c50ba25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9155e905785b48d3a58fabd03e2ed04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图,已知点
是边长为1的等边
内一点,满足
,过点
的直线
分别交
,
于点
,
.设
,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/4f0d53573554894dbe3b31027d7cdfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c9ca024d66f87e779fee3922c3b37b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
A.![]() | B.点![]() ![]() |
C.![]() | D.![]() |
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2021-07-11更新
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4卷引用:广东省广州市第四十一中学2021-2022学年高一下学期4月月考数学试题
广东省广州市第四十一中学2021-2022学年高一下学期4月月考数学试题(已下线)专题02 平面向量的相关计算(中档题)-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)山东省潍坊市2020-2021学年高一下学期期末数学试题湖北省黄冈市蕲春县2021-2022学年高二上学期期中数学试题
21-22高一下·上海浦东新·阶段练习
名校
9 . (1)已知
为
外接圆的圆心,若
,
,则
是否为定值?若是,求出这个值;若不是,请说明理由;
(2)若点D为边BC上一点,点E为边AC中点,AD与BE交于点P,且
.若
(x、
),求x、y的值.
![](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/f371c0b1d573c06516ab1904d95ee49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54c556458d8075aa2d133615725f8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56f3ad7839112bd580857479d253883.png)
(2)若点D为边BC上一点,点E为边AC中点,AD与BE交于点P,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10bc9e1a36293cca8dc7c5297b17736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f92aef16f5f17f7613e92f34c38e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
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名校
10 . 下列说法不正确的有( )
A.若向量![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.任意一条直线都有倾斜角和斜率; |
D.若平面上一点![]() ![]() ![]() ![]() |
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