23-24高二下·江苏·课前预习
解题方法
1 . 如图,在直三棱柱
中,
,棱
,N为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/c7630813-7f01-4f9f-9ad4-5585ef680a59.png?resizew=131)
(1)求
的长;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84efd0032219979f6e893e977f6229ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/c7630813-7f01-4f9f-9ad4-5585ef680a59.png?resizew=131)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e374399249243b5ca1cb0bcc5e85c6a.png)
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2 . 已知正四面体
的棱长为1,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/c42e4aa3-9c9e-4901-acad-e46690ef61bb.png?resizew=159)
(1)确定向量
在直线
上的投影向量,并求
·
;
(2)确定向量
在平面
上的投影向量,并求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd7c1e8a85c466f89cd99da71579787.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/c42e4aa3-9c9e-4901-acad-e46690ef61bb.png?resizew=159)
(1)确定向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
(2)确定向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef2723673c90347f6dd58346278c7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd7c1e8a85c466f89cd99da71579787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
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23-24高二下·江苏·课前预习
3 . 如图,正三棱柱
的各棱长都为
,
、
分别是
、
的中点,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/1af18b93-4fe5-40e7-9a1d-4a1444debd30.png?resizew=108)
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4 . 如图,在直三棱柱
中,
,
,则向量
与
的夹角是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99135167175760935148047d6170c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4979f0d8ed02ce99f440b6ff4f3216e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38dfb3f3d83fa111eb89009789e88b1.png)
A.30° | B.45° |
C.60° | D.90° |
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23-24高二上·全国·课前预习
5 . 已知平行六面体
的各棱长均为1,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/40968ef3-9271-4beb-b9ac-0d71a46c15dc.png?resizew=173)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab00669c57efe0b65ae5430029ee090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6537894bee5cd52519890b95f9ecdf2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/40968ef3-9271-4beb-b9ac-0d71a46c15dc.png?resizew=173)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,在平行六面体
中,
,
,
,
,
.求:
;
(2)
的长(精确到0.1).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598098f91b9ad36cf04a7f839761f93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97a83c7bc0b91016f61a43833042d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
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2023-09-19更新
|
350次组卷
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3卷引用:专题01 空间向量的线性运算(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)
(已下线)专题01 空间向量的线性运算(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)人教A版(2019)选择性必修第一册课本例题1.1 空间向量及其运算四川省成都市金牛区实外高级中学有限公司2023-2024学年高二上学期第一阶段考数学试题
7 . 如图所示,已知直三棱柱
中,D为
的中点,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca3bcd5969d38d0882fe98865e91464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a77a34247178a94ce97827b1d5adab5.png)
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名校
8 . 如图,平行六面体
所有棱长都为1,底面
为正方形,
.则对角线
的长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecbca919bff5a39a99dd7f867dd61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/9/63ba4b43-5231-4889-949a-bef0821436a5.png?resizew=177)
A.![]() | B.![]() | C.2 | D.![]() |
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1360次组卷
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8卷引用:专题01 空间向量的线性运算(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)
(已下线)专题01 空间向量的线性运算(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)内蒙古自治区包头市2022-2023学年高二上学期期末理科数学试题新疆维吾尔自治区塔城地区第一高级中学2023-2024学年高二上学期9月月考数学试题重庆市涪陵区部分学校2023-2024学年高二上学期第一次月考数学试题(已下线)1.1.2 空间向量的数量积运算【第二课】贵州省六盘水市纽绅中学2023-2024学年高二上学期10月月考数学试题(已下线)第一次月考检测模拟试卷(原卷版) 四川省泸县第五中学2023-2024学年高二上学期第一次月考试数学试题
2023高二·全国·专题练习
9 . 两个向量的夹角
(1)定义:已知两个非零向量
,作
,则
叫做
与
的夹角;
(2)范围:夹角
的取值范围是_________ .
①当
与
同向时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
_______ ;②反向时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
_____ ;③当
与
垂直时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
_______ ,并记作
.
(1)定义:已知两个非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cefb3de8805e7febdf23b4e959d9711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7e00f8bacce4d649b535449f04568c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
(2)范围:夹角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
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名校
解题方法
10 . 已知平行六面体
如图所示,其中
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade3909a2df36df95550ff040feb7dd.png)
,线段AC,BD交于点O,点E是线段
上靠近
的三等分点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/fe761bbc-bc7c-4dcc-aa44-70b444cfa29a.png?resizew=190)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade3909a2df36df95550ff040feb7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76c7dc8aaa8f8aa1bda6ef0b4df5343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/fe761bbc-bc7c-4dcc-aa44-70b444cfa29a.png?resizew=190)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-04-26更新
|
861次组卷
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7卷引用:1.1.2 空间向量的数量积运算(导学案)-【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)1.1.2 空间向量的数量积运算(导学案)-【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)安徽省池州市第一中学等2校2022-2023学年高二下学期3月月考数学试题(已下线)模块三 专题1 空间向及其运算 B能力卷(已下线)第一章:空间向量与立体几何章末综合检测卷-【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07讲 空间向量的数量积运算9种常见考法归类(2)(已下线)模块三 专题1 空间向及其运算 B能力卷 (人教B)(已下线)3.2空间向量与向量运算(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)