解题方法
1 . 已知三棱柱
中,棱长均为
,顶点
在底面
上的射影恰为
的中点
,
为
的中点,则直线
与直线
所成角的余弦值为________ .
![](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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/2021/6/24/2750005077688320/2781071884288000/STEM/a108ec1d-4115-45c0-9e0b-35de727577b8.png?resizew=233)
您最近一年使用:0次
2021-08-07更新
|
1401次组卷
|
5卷引用:浙江省宁波市九校2020-2021学年高一下学期期末联考数学试题
浙江省宁波市九校2020-2021学年高一下学期期末联考数学试题(已下线)第09讲 空间点、直线、平面之间的关系(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)第02讲 基本图形的位置关系(3)浙江省温州市瑞安市第六中学2021-2022学年高一下学期5月月考数学试题(已下线)专题04 立体几何初步(1)-【常考压轴题】
名校
解题方法
2 . 在
中,设
,
,
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edb4ffd300dbd7dfdcc5a751f79c482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c748c4c6d9c1e5c16a8ed47f0792f5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325ba8093bd40f00a79e3c49010ea704.png)
A.若![]() ![]() |
B.![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2021-08-07更新
|
1321次组卷
|
3卷引用:江苏省南通市2020-2021学年高二下学期期末数学试题
名校
3 . 已知非零平面向量
,
,
满足:
,
的夹角为
,
与
的夹角为
,
,
,则
的取值范围是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002e032096066a5a4a10e6d8b4fa9694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602a90ff1c1c83b1c237553f1940262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa583c68f70bcf0c819cb78cce2ac38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5a9bd10df34bffb7b63ea0477be7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3cbad2f594e5a09a40c0634b6ead7a.png)
您最近一年使用:0次
2021-08-07更新
|
1208次组卷
|
7卷引用:浙江省温州市共美联盟2020-2021学年高二下学期期末数学试题
浙江省温州市共美联盟2020-2021学年高二下学期期末数学试题四川省内江市市中区第六中学2021-2022学年高二上学期创新班入学考试数学试题(已下线)专题4-1 三角函数性质、最值和w小题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)重难专攻(六) 平面向量的最值问题 B素养提升卷(已下线)重难点突破03 最全归纳平面向量中的范围与最值问题 (十大题型)-1福建省厦门第一中学2023-2024学年高一下学期第一次适应性训练(月考)数学试题福建省厦门第一中学2023-2024学年高一下学期第一次适应性数学试题
名校
4 . 如图,在正四棱锥
中,
.从
拉一条细绳绕过侧棱
和
到达
点,则细绳的最短长度为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4178e3039c356bd376249a19cdf94bc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2021/7/3/2756462633484288/2780367304761344/STEM/f1eacda81cd74c17abbad29298d8c77a.png?resizew=221)
您最近一年使用:0次
2021-08-06更新
|
957次组卷
|
7卷引用:湖北省十堰市2020-2021学年高一下学期期末数学试题
解题方法
5 . 已知三棱锥
,
平面ABC,
,
,则该三棱锥外接球的半径为___________ ;若此三棱锥可以在正方体中任意转动,则该正方体的最小体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cec47797c4c6133082bda5b0b63ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
您最近一年使用:0次
2021-08-06更新
|
616次组卷
|
2卷引用:河北省廊坊市2020-2021学年高一下学期期末数学试题
解题方法
6 . 已知
中,
,
,
,
为
内一点,且
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1082dd7e08556354aa7d4861d419e4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9dab0293dbad92fe84bad6b0d957bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/f5d4e1907aa9e78993f8df9aa96cd547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
解题方法
7 . 如图,等腰直角三角形地块
,
,为了美化环境,现对该地块进行改造,计划从
的中点
引出两条成
角的射线,分别交
,
于点
,
,将四边形
区域改造为人工湖,其余区域为草地,设
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264566177792/STEM/eb921c4e-3326-4350-9955-a87dadf4bddb.png?resizew=304)
(1)当
时,求草地
的面积;
(2)求人工湖
的面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa3c20ca003f7c7a916bb48d4de96c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a61d8bedef61745ee4fd89a8c0c119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b0668257abc308c6d23354ab663814.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264566177792/STEM/eb921c4e-3326-4350-9955-a87dadf4bddb.png?resizew=304)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求人工湖
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a61d8bedef61745ee4fd89a8c0c119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
您最近一年使用:0次
解题方法
8 . 在
中,角
的对边分别为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/c808a7e3-f657-4bb2-afc3-e8beffd8edc8.png?resizew=232)
(1)已知
,且 (在①
,②
,③
,这三个条件中任选两个补充到横线上),求
;
(2)若
,
,
与
交于点
,过
的直线分别交线段
于
两点,设
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95d62b9a1fc994c972781c7013fedba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46d2380152e6efc40909dad0ae96c12.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/c808a7e3-f657-4bb2-afc3-e8beffd8edc8.png?resizew=232)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05e0b24aa92137350a194a062b9727c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2f1318b4bb40a1ec855834ec7e61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36ec31cfd615abfbee3ed2f4a1d8883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57770796a401eef8d7144a98a42ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f78e25ebfe9c30ad05fbf224ca32118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13c0c473e41134024b3f40612d320df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b5126cbc748e852c2c39ca0ed232aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d4cadeffffd9480a95a17109570dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b999f0d44be7a9d3aa85a0d41a1a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9912589c7030e0226dacc5596a5605dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaacfaef44a654c0a1c283ef03fc0550.png)
您最近一年使用:0次
名校
9 . 如图,已知正四棱锥
与正四面体
所有的棱长均为
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759751319707648/2777760744325120/STEM/ede128cb-f7cd-45e0-b834-efbf130c4aef.png?resizew=477)
(1)若
为
的中点,证明:
平面
;
(2)把正四面体
与正四棱锥
全等的两个面重合,排成一个新的几何体,问该几何体由多少个面组成?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858d5bfe390d0cb79cee200241240a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759751319707648/2777760744325120/STEM/ede128cb-f7cd-45e0-b834-efbf130c4aef.png?resizew=477)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d50356a01ae13936f1bd8efa94c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)把正四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858d5bfe390d0cb79cee200241240a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
您最近一年使用:0次
2021-08-02更新
|
894次组卷
|
3卷引用:福建省福州市2020-2021学年高一下学期期末数学试题
10 . 甲烷是一种有机化合物,分子式是
,它作为燃料广泛应用与民用和工业中,近年来科学家通过观测数据,证明了甲烷会导致地球表面温室效应不断增加,深入研究甲烷,趋利避害,成为科学家面临的新课题,甲烷分子的结构为正四面体结构,四个氢原子位于正四面体的四个顶点,碳原子位于正四面体的中心,碳原子和氢原子之间形成的四个碳氢键的键长相同,键角相等,请你用学过的数学知识计算甲烷碳氢键之间的夹角余弦值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff19349a80467d65564cc2953f0c978.png)
您最近一年使用:0次