名校
1 . 如图,三棱锥
中的三条棱
两两互相垂直,
,点
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/7ab9e002-ef32-4e3e-b432-a420b0aaa507.png?resizew=158)
(1)证明:
平面
.
(2)若
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1361092e790e4154a14aea9d0db65a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea6ce40f9bd9083dd8e40822f21ebb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe9b0c00cab139524b79ab2847e462e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/7ab9e002-ef32-4e3e-b432-a420b0aaa507.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42de572d68ded125eccccc512c4fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-10-10更新
|
1688次组卷
|
3卷引用:河南省周口市项城市第三高级中学2023-2024学年高二上学期第一次月考数学试题
解题方法
2 . 已知
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c56d479e3620d764eccab05fe0a1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e076b91a9178217532e11c496400e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8444d63d1ca92651c62fe9b220859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea730233033e2fca0bce6a369a32582f.png)
您最近一年使用:0次
解题方法
3 . 已知两条不重合的直线m,n和平面
都垂直.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0205571fa39f343ee5749b78d466bf0.png)
您最近一年使用:0次
解题方法
4 . 如图,已知平面
,
,直线
平面
,且
平面
.求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa807136194c18d3ac58902c67f9333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/65bb0b48-a810-4828-8f53-423ccc862ef7.png?resizew=164)
您最近一年使用:0次
解题方法
5 . 已知AB,AC分别是平面
的垂线和斜线,BC是AC在
内的射影,
且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3777318aa3fbdee09cfeeea971e8fcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95e692badf11ca5ac25104a166f4467.png)
您最近一年使用:0次
6 . 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)
您最近一年使用:0次
解题方法
7 . 已知正方体
的棱长均为1.
(1)求
到平面
的距离;
(2)求平面
与平面
之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5bef4c4586630701fae5fa141c8818.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5bef4c4586630701fae5fa141c8818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43713ea7ad8151c6d035f9c7c63996d0.png)
您最近一年使用:0次
解题方法
8 . 已知
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56668df8478e0d1648be71fc40b7d4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10d07400f5b702af6cffb46e06721e3.png)
您最近一年使用:0次
23-24高二上·上海·课后作业
解题方法
9 . 利用向量证明:如果一条直线垂直于一个平面内的两条相交直线,那么这条直线垂直于这个平面(即垂直于这个平面中的任何直线)
已知:如图,
、
是平面
内的两条相交直线,直线
满足
,
.求证:
.
已知:如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff290c28b42c8380283f6259daaec5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac16b6d9ffc65507c5cd4083a1363937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
您最近一年使用:0次
2021高二·全国·专题练习
10 . 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)
您最近一年使用:0次
2023-09-04更新
|
1111次组卷
|
8卷引用: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)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(已下线)6.3 空间向量的应用 (2)