2024高三·全国·专题练习
解题方法
1 . 已知在正四棱柱
中,
,
,E为
的中点,F为
的中点.求证:
(1)
且
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8395ad704eb0d1e66f7c2e1558de34ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1025ae64ab3bbc38c0a9adbb8ef73e13.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68c2e813588fdb7357757199992350.png)
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2 . 如图,在平行六面体
中,
,
,
,
,
,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/2cbb9c5d-de80-4e31-ace2-02ec91679411.png?resizew=166)
(1)
;
(2)
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5600c2061f6e12991bf271a4a3ab51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cfd839b35f8db9d0f5b588679c6b3f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/2cbb9c5d-de80-4e31-ace2-02ec91679411.png?resizew=166)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebbf35fa5d3b105ca1e86456480d49d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
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名校
3 . 已知空间向量
.
(1)求
;
(2)判断
与
以及
与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9be0ea19a65bf3f4e2a45cb84575a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884e8f2d5835771fd49093a6709be3a0.png)
(2)判断
![](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/7b76118bdca6c463cfb19b66f30281c4.png)
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4 . 如图,在平行六面体
中,以顶点A为端点的三条棱长度都为1,且两两夹角为
.记
,
,
.
(1)求
的长;
(2)求
与
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/746db900-5dfd-4b4a-9826-c73b22316a0e.png?resizew=179)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccec46f7c4da972fef6e940158628242.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccec46f7c4da972fef6e940158628242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
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2023-11-21更新
|
1088次组卷
|
4卷引用:四川省南充高级中学2023-2024学年高二上学期11月期中考试数学试题
四川省南充高级中学2023-2024学年高二上学期11月期中考试数学试题(已下线)专题01 空间向量及其应用常考题型归纳(1)(已下线)第6章 空间向量与立体几何单元综合测试卷-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)江苏省扬州市广陵区红桥高级中学2023-2024学年高二下学期3月月考数学试题
5 . 如图,给定长方体
,
,
,点
在棱
的延长线上,且
.设
,
,
.
(1)试用
表示向量
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6155f82a6f64b20085976cea9b64193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6480f4f44375d85b8c03d816977ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef36fa79d02dd76e9ac5fda1689268f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9206f052cc7298fdf9049f9386f53928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381985fdee6a1ac3ad4a73f5f653b84c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/532e5f6b-25b5-4495-8d97-26eb44fdea33.png?resizew=165)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d71331dc768e2788b5ff67b86d2e5fc.png)
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6 . 已知向量
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c2778f71620688347ec8577d5f0417.png)
(1)求
的值;
(2)求
;
(3)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8ec3c4d9c23b3534a2becab854ca30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8d5150c7ccd9958d4011510bd79b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c2778f71620688347ec8577d5f0417.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89524bf50baf4afe651a5e0f94a5e18.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d07c8f31afcf0c695a3530e0c3ba51.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5382bd3fda4371289ce6800f71f9565.png)
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2023-10-17更新
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971次组卷
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3卷引用:北京市第一六一中学2023-2024学年高二上学期阶段练习数学试题
23-24高二上·全国·期中
7 . 已知
,
,求
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6161c5738a90390c0c24d53acd15472b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48041c37f264312e21286697258cf889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca35e52b8430246a1cf96e9e617cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39d1d88189726ae99c309644fca3494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572219f08b22b82248507b4ddb9f2e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd97b5d04889c36ec9b81b62d3d0736.png)
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23-24高二上·上海·课后作业
8 . 在
中,已知
,
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d440191ea075edc85fe0d15c35d36bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46b66fcb9e3b39bb4c0787c9def023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
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22-23高二下·全国·课后作业
名校
解题方法
9 . 如图所示,在120°的二面角
中,AC⊂α,BD⊂β且AC⊥AB,BD⊥AB,垂足分别为A,B,已知AC=AB=BD=6,试求线段CD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ce3f859c6b9a0cfc98bdf5b3d0f395.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/23/cec75c87-df69-46da-8e35-8a37ff27b377.png?resizew=164)
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2023-05-20更新
|
489次组卷
|
7卷引用:6.3.4空间距离的计算(1)
(已下线)6.3.4空间距离的计算(1)(已下线)模块三 专题1 空间向及其运算 A基础卷(已下线)第07讲 空间向量的数量积运算9种常见考法归类(1)(已下线)模块三 专题1 空间向及其运算 A基础卷(人教B)(已下线)1.1.1 空间向量及其运算(分层练习)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第一册)内蒙古自治区呼和浩特市土默特中学2023-2024学年高二上学期期中数学试题(已下线)专题01空间向量及其运算(4个知识点8种题型3个易错点)(2)
10 . 如图,在平行六面体
中,E,F分别为棱
,CD的中点,记
,
,
,满足
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/3154ab91-a1a3-41e0-9e1f-ef780d0979ab.png?resizew=213)
(1)用
,
,
表示
;
(2)计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20cbdfe479954ba2bc33142bc931c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066bca5c293e81c8579c85cb365c4a34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4654966ec154b40a92fab6fa5390542a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5e5c0d0bcecfefc6ce763098a3ddc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6627c2c12eb6deddcd3585bf6cd7337c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93b4787448ee5858e81109cc208b7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc32568a310f81981445ca7385b03ee4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/3154ab91-a1a3-41e0-9e1f-ef780d0979ab.png?resizew=213)
(1)用
![](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/cdc78f89939084f4979069d2d5b45833.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff4faea020790092dc1629e62bf006c.png)
您最近一年使用:0次
2023-04-30更新
|
1382次组卷
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13卷引用:四川省成都市蓉城高中联盟2022-2023学年高二下期期中考试理科数学试题
四川省成都市蓉城高中联盟2022-2023学年高二下期期中考试理科数学试题(已下线)模块三 专题2 空间向量的基本定理 A基础卷(已下线)1.1.2 空间向量的数量积运算 精讲(4大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)第08讲 空间向量基本定理7种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)第07讲 空间向量的数量积运算9种常见考法归类(1)(已下线)1.2 空间向量基本定理(分层作业)(3种题型分类基础练+能力提升综合练)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)(已下线)模块三 专题2 空间向量的基本定理 A基础卷(人教B)(已下线)3.3.1空间向量基本定理表示(同步练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)四川省成都石室阳安学校2023-2024学年高二上学期10月月考数学试题陕西省西安市周至县第四中学2023-2024学年高二上学期第一次月考数学试题四川省成都市新津区成外学校2023-2024学年高二上学期10月月考数学试题(已下线)1.2 空间向量基本定理【第一练】(已下线)专题4 大题分类练(空间向量与立体几何)基础夯实练 高二期末