名校
解题方法
1 . 已知棱长为1的正方体
,以正方体中心为球心的球
与正方体的各条棱相切,若点
在球
的正方体外部(含正方体表面)运动,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
A.2 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-13更新
|
437次组卷
|
2卷引用:江苏省盐城中学2023-2024学年高二下学期5月阶段性质量检测数学试题
2024高二·全国·专题练习
2 . 已知
,空间向量
为单位向量,
,则空间向量
在向量
方向上投影的模为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145a7e8f352fab613b773dc6639b508b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739c4e6d5dfaccd771be4dd5e0e17c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
您最近一年使用:0次
23-24高二下·江苏·课前预习
解题方法
3 . 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)
您最近一年使用:0次
4 . 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)
您最近一年使用:0次
23-24高二下·江苏·课前预习
5 . 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)
您最近一年使用:0次
6 . 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° |
您最近一年使用:0次
23-24高二下·江苏·课前预习
解题方法
7 . 已知
,
是相互垂直的单位向量,则
=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952ca1ac93bb1a68c43b663732f38030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02bd32ab64d9c9cdf154e86e5eb59c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
A.1 | B.2 |
C.3 | D.4 |
您最近一年使用:0次
8 . 在正四面体
中,棱长为2,且E是棱
中点,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53a042dac85b32a172b198bd9d6c986.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 在四棱柱
中,四边形
为平行四边形,若
,
,
均为单位向量,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293e306e9ad08bd8f00562fd0d9975a7.png)
____________ .
![](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/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d507cbc45fbda1630807543d4e038bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e6dadd08e418d154940177e9a474fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293e306e9ad08bd8f00562fd0d9975a7.png)
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10 . 在棱长为2的正四面体ABCD中,E,F,G分别是棱AB,AD,DC的中点.则下列各式成立的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次