23-24高一下·全国·课后作业
解题方法
1 . 已知
,向量
,
,
满足条件
,
.求证:
是等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ac2dd55fa98f9bf10fcd95ce3169c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96cb7ee166966ed0b1605c263e433cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc77d6da6e8f3ad5c239e7cc6c9930c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed22ce98b22693a90269d933bb6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2f40e5abdb1a6638af538d1b87dd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b60a6fd3830554a0e5e31123a711e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ac2dd55fa98f9bf10fcd95ce3169c3.png)
您最近一年使用:0次
解题方法
2 . 已知
,
是两个非零向量,当
(
)的模取最小值时.
(1)求
的值;
(2)求证:
.
![](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/edc20644e220b5abd6ca29a666760dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92864b1adfe473942d40eb958d35a20d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc8202c666090383cab0711b616aed1.png)
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解题方法
3 . 已知非零平面向量
,
的夹角为
,
.
(1)证明:
;
(2)设
,求
的最小值.
![](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/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b8c74852e27857e82eb14292f055b3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f5649d87ad075cd59a6db7da93af4d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d882913c702822a27f07c06ea005a1f.png)
您最近一年使用:0次
2023-01-03更新
|
947次组卷
|
3卷引用: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)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)北京市2023届高三“极光杯”跨年线上测试数学试题第九章 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)
解题方法
4 . 如图,已知
为直角三角形,
所对的边分别为a,b,c,
若沿AB及AC方向的两个力
的大小分别为
.
![](https://img.xkw.com/dksih/QBM/2022/8/22/3049859291734016/3050051743793152/STEM/d5ea0081896243f9baecd572c5eb04be.png?resizew=196)
(1)试求
的大小;
(2)求证:
的方向与
的方向相同.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0196750bbea53c91e3a3f2bde088f893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c66fcf11b5181ac94bc31722eb2ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e3568de0148dc9c5c853b2a4cb50fb.png)
![](https://img.xkw.com/dksih/QBM/2022/8/22/3049859291734016/3050051743793152/STEM/d5ea0081896243f9baecd572c5eb04be.png?resizew=196)
(1)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a498a1eae64a4edc6540acddb89f962.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a498a1eae64a4edc6540acddb89f962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f4ddbb8959f904d71259be7c6ab36.png)
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21-22高一·湖南·课后作业
5 . 设向量
,
,其中
.
(1)求证:
与
互相垂直;
(2)若
与
(其中
)大小相等,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb2a6ac6bb1cb11445577dd97e0fa30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5109992a5bf54faa23355741beb74959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b85478bd7295db8fbab462e5f9db1e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1c1dd6b13d92f2cc2eef097e14c07c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41960bbc66bdc3b28be0138f83f9de5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496590f060e41cbaca42b9eaca3cc6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
您最近一年使用:0次
解题方法
6 . (l)求证:
;
(2)已知向量
、
满足:
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22a8f2a379b9beae45d0b71ec76fd55.png)
(2)已知向量
![](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/89d5b0d278a7457a0c548278c60ab695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae53138d68ff01830a88ba2876ef951f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeabd4eaeb049715deefc72182c0ef1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811e6a5941a72ea39cf9cb8679344c4.png)
您最近一年使用:0次
名校
解题方法
7 . 如图1,在
中,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768347493367808/2793235123027968/STEM/be0630e5f8ae48e68c0a29fbba31cc8e.png?resizew=227)
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768347493367808/2793235123027968/STEM/19754a8e6b13471b8b84c2f358039557.png?resizew=211)
(1)求证:
;
(2)直线
过点
且垂直于
,
为
上任意一点,求证:
为常数,并求该常数;
(3)如图2,若
,
为线段
上的任意一点,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca28df653d8978421b92c94e40a4fa29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a629d5890083cc3d5a9e519745d164f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768347493367808/2793235123027968/STEM/be0630e5f8ae48e68c0a29fbba31cc8e.png?resizew=227)
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768347493367808/2793235123027968/STEM/19754a8e6b13471b8b84c2f358039557.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6965913d55d82f1055431b4852cad20.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cf48675aa4ca725dcf8c2bbd1ac052.png)
(3)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d2c413253fe5bc1f9287a35e6fc45eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b583edc9095a2111e993fd3a28a260.png)
您最近一年使用:0次
2021-08-24更新
|
459次组卷
|
3卷引用:6.4.1 平面向量在几何和物理中的运用(精练)-2021-2022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)6.4.1 平面向量在几何和物理中的运用(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)江苏省常州市前黄高级中学2020-2021学年高一下学期3月学情检测数学试题(已下线)6.4.1平面几何中的向量方法+6.4.2向量在物理中的应用举例(精练)-【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)
解题方法
8 . 已知
是两个单位向量,
,
,
,
.
(1)若
,求
;
(2)若
,求
的最大值及相应的
值;
(3)若
,
,求证:
.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaccfa28fcd8b60194990aca32418470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b307e7885a99d20f3f5cdeb22b5321b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300ac50f6c88b25c6c083309913eecbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cfbefa60582db308925afcd5a8a42e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a62ed270b6d736b9fcfbb6f8425699f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07bd57dd68879c0d78a2c42b9e724584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec223312cbc1aa48586f94fd03232d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abd7755b18fc0d7bbb014b1c5936f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2490175a5a77617d7e22087a7f11ead9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e287bb061bde44afaab70747ffe18769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152d4811e2f1341399c1cfa77f6e8d23.png)
.
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名校
解题方法
9 . 如图,在边长为1的正△ABC中,E,F分别是边AB,AC上的点,若
=m
,
=n
,m,n∈(0,1).设EF的中点为M,BC的中点为N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3421342d-9d53-41b5-a727-590904a9afb4.png?resizew=186)
(1)若A,M,N三点共线,求证:m=n;
(2)若m+n=1,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd0cecf5c102254b9755e42a80c3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b8a2a41a8b50e10d68943e3f0f4e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/3421342d-9d53-41b5-a727-590904a9afb4.png?resizew=186)
(1)若A,M,N三点共线,求证:m=n;
(2)若m+n=1,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfe64604ee828d439929c94c205c51c.png)
您最近一年使用:0次
2021-10-20更新
|
710次组卷
|
12卷引用:8.1 向量的概念和线性运算(作业)-【上好课】2020-2021学年高一数学下册同步备课系列(沪教版2020必修第二册)
(已下线)8.1 向量的概念和线性运算(作业)-【上好课】2020-2021学年高一数学下册同步备课系列(沪教版2020必修第二册)沪教版(2020) 一轮复习 堂堂清 第六单元 6.2 向量的分解定理上海市第二中学2019-2020学年高二上学期期中数学试题四川省眉山市彭山区第一中学2019-2020学年高一下学期期中考试数学试题(已下线)专题6.4 平面向量的应用--几何、物理(B卷提升篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版,浙江专用)江苏省苏州市三中2020-2021学年高一下学期3月月考数学试题江苏省镇江市第一中学2020-2021学年高一下学期期中数学试题山东省枣庄市薛城区2020-2021学年高一下学期期中考试数学试题山东省枣庄市第八中学2020-2021学年高一下学期期中考试数学试题山东省济宁市兖州区2021-2022学年高一下学期期中数学试题山东省滨州市博兴县第二中学2022-2023学年高一下学期第二次月考数学试题四川省凉山州民族中学2023-2024学年高一下学期3月月考数学试题
10 . 利用向量的数量积证明如下结论.
(1)长方形的两条对角线相等;
(2)平行四边形对角线的平方和等于四边的平方和.
(1)长方形的两条对角线相等;
(2)平行四边形对角线的平方和等于四边的平方和.
您最近一年使用:0次
2020-02-04更新
|
326次组卷
|
3卷引用:人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积 8.1.2 向量数量积的运算律
人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积 8.1.2 向量数量积的运算律(已下线)第八章 向量的数量积与三角恒等变换 8.1 向量的数量积 8.1.2 向量数量积的运算律人教B版(2019)必修第三册课本习题8.1.2 向量数量积的运算律