名校
解题方法
1 . 如图,在空间直角坐标系
中,四棱柱
为长方体,
,点
为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd407cdb6c758cdbe7e7216544f85b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce34c05c1445e027e9fc009907046e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c8b9d5680c06f9e28c311d67cfadd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://img.xkw.com/dksih/QBM/2024/3/28/3463332106461184/3464077086294016/STEM/502a38b4235b41deb5e06261ecf054f3.png?resizew=168)
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解题方法
2 . 如图,直三棱柱
中,
,
是
的中点,
是
的中点.
直线
;
(2)求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46720eabe78e309e02c24678632b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7c79e163af35ecc1997fa48412af36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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2024-03-24更新
|
1373次组卷
|
3卷引用:上海市宝山中学2023-2024学年高二下学期3月考数学试卷
上海市宝山中学2023-2024学年高二下学期3月考数学试卷甘肃省武威市凉州区2023-2024学年高二下学期期中质量检测数学试卷(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
2024高三·全国·专题练习
解题方法
3 . 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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2024高三·全国·专题练习
解题方法
4 . 如图,在正方体
中,
,
,
,点M,N分别是
,
的中点.
(1)试用
,
,
表示
.
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a08f3a88dffed011df93d1d606a08ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f8173bb7787b6b107acfe767dd1d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232311b4261c36b659555a07bfa00f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/d1ed7a47-813c-483a-a098-5d06cabb43a5.png?resizew=171)
(1)试用
![](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/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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名校
5 . 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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2023-12-15更新
|
734次组卷
|
5卷引用:专题12 空间向量的坐标表示8种常见考法归类-【寒假自学课】2024年高二数学寒假提升学与练(苏教版2019)
(已下线)专题12 空间向量的坐标表示8种常见考法归类-【寒假自学课】2024年高二数学寒假提升学与练(苏教版2019)(已下线)高二数学上学期第三次月考模拟卷(空间向量与立体几何+直线与圆的方程+圆锥曲线方程+数列)(原卷版)(已下线)6.2 空间向量的坐标表示(2)山东省菏泽市鄄城县第一中学2023-2024学年高二上学期12月月考数学试题(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
名校
6 . 如图,在直四棱柱
中,
,
,
,E,F,G分别为棱
,
,
的中点,建立如图所示的空间直角坐标系.
(1)求
的值;
(2)证明:C,E,F,G四点共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a114031e9fd808124cf218d82d5cdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/88706f8c-b39d-41f9-a3ae-4ff60a08d07d.png?resizew=260)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf2922c94338fb5c91b8c1ff9bb7e34.png)
(2)证明:C,E,F,G四点共面.
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2023-11-26更新
|
443次组卷
|
3卷引用: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)
(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月月考数学试题陕西省咸阳市礼泉县2023-2024学年高二上学期期中学科素养调研数学试题
名校
7 . 如图,在直三棱柱中,
,
,
,
,
分别是
,
的中点.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b201f1e798eb74963b98f2b0da4132.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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8 . 如图,已知正方体
中
,
的坐标分别为
,
,
,
.分别求平面
与平面
的一个法向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65183d238c9bc2be73770717d890683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a42bc893aeabafad84da3e66e73f885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b11c6835301f2b6b8b3f50797dc434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5738e712c599c54aebca0d4a3d9fcf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359da7e284844965b9bb9121f5c43bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/effc782c-e29f-4170-9e09-6ea43e169a92.png?resizew=178)
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2021高二·全国·专题练习
9 . 如图所示,在四棱锥
中,底面是直角梯形,
,
⊥底面
,且
,
,建立适当的空间直角坐标系,分别求平面
与平面
的一个法向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca27f9fa673fa014bb34f92355d6714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffbcd82b98a9ae69aa4ee28bb49a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2a52f691259e1a747d356f631c3d3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/5/aa36d977-d9b2-42a3-b754-a6cb97a7d1a8.png?resizew=179)
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2023-09-04更新
|
1113次组卷
|
8卷引用:6.3 空间向量的应用 (2)
(已下线)6.3 空间向量的应用 (2)(已下线)专题1.9 空间向量的应用-重难点题型精讲-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)1.4.1 第1课时 空间向量与平行关系(学案)-2021-2022学年高二数学教材配套学案+课件+练习(人教A版2019选择性必修第一册)(已下线)第七课时 课后 1.4.1.1 空间中点、直线和平面的向量表示(已下线)专题08 直线的方向向量与平面的法向量(重点突围)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)(已下线)2.4.1 空间直线的方向向量和平面法向量(同步练习)-【素养提升—课时练】2022-2023学年高二数学湘教版选择性必修第二册检测(基础篇)北师大版(2019) 选修第一册 数学奇书 第三章 空间向量与立体几何 §4 向量在立体几何中的应用 4.1 直线的方向向量与平面的法向量海南省川绵中学2023-2024学年高二上学期10月第一次月考数学试题
名校
10 . 在图1中,四边形
为梯形,
,
,
,
,过点A作
,交
于
.现沿
将
折起,使得
,得到如图2所示的四棱锥
,在图2中解答下列两问:
的体积;
(2)若F在侧棱
上,
,求证:二面角
为直二面角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6610676353016a9f7235d306b731c1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df793f5dac174bc71bd1e82bbf5732b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5b4ea605cf0b98e428d071f6be6762.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4999d4fbcbe15f78c29d518f25d317c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99be23ddbd80e2c75649e3d1f8594130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99be23ddbd80e2c75649e3d1f8594130.png)
(2)若F在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386e945cb8ffa5288ba68b0714ea9e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade6931be0db4f7a771bb764c88c80d9.png)
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2022-11-24更新
|
915次组卷
|
5卷引用:浙江省遂宁市私立宏达高级中学2023-2024学年高二下学期3月月考数学试题