名校
1 . 如图,AB是
的直径,PA垂直于
所在的平面,C是圆周上不同于A,B的一动点.
面PAC;
(2)若PA=AC=1,AB=2,求直线PB与平面PAC所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)若PA=AC=1,AB=2,求直线PB与平面PAC所成角的正切值.
您最近一年使用:0次
2021-01-29更新
|
3994次组卷
|
10卷引用:内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高一下学期期末考试数学试题
内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高一下学期期末考试数学试题宁夏六盘山市高级中学2020-2021学年高一上学期期末考试数学试题吉林省长春市第二十中学2020-2021学年高一下学期期末数学试题新疆乌鲁木齐市第三十六中学2022-2023学年高一下学期期末考试数学试题新疆阿克苏地区新和县实验中学2021-2022学年高二上学期期末数学试题专题05 空间直线、平面的垂直-《期末真题分类汇编》(新高考专用)(已下线)8.6 第八章 《立体几何初步》 综合测试卷--2020--2021高中数学新教材配套提升训练(人教A版必修第二册)(已下线)8.6空间直线、平面的垂直(2)(精炼)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)广东省东莞市新世纪英才学校2020-2021学年高一下学期第二次段考数学试题4.3.2 直线与平面垂直的性质
名校
解题方法
2 . 如图,底面是正三角形的直三棱柱
中,
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2021/1/6/2630389057699840/2636484663451648/STEM/2ce55197-db2f-42cf-8d81-5c47209afcd8.png)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/2021/1/6/2630389057699840/2636484663451648/STEM/2ce55197-db2f-42cf-8d81-5c47209afcd8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07391ef575d28f09bc5cda0ff8130a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7caf5cf7af17598e879101cf25f7de9.png)
您最近一年使用:0次
2021-01-15更新
|
198次组卷
|
3卷引用:内蒙古赤峰市2020-2021学年高一下学期期末数学(文)试题(B )
名校
解题方法
3 . 如图,在四棱柱
中,
底面
,
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/2020/12/23/2620376477532160/2624498471206912/STEM/8937d8023fe44b6292f49b2e1a3f90ec.png?resizew=227)
(1)求证:平面
平面
;
(2)求二面角
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb026347fc22a3f8211e8366c0468c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba263fb3fdfb5fc82234795dd052f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486be8401949a5f1fab18ae0d7d9aa9c.png)
![](https://img.xkw.com/dksih/QBM/2020/12/23/2620376477532160/2624498471206912/STEM/8937d8023fe44b6292f49b2e1a3f90ec.png?resizew=227)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21daa1cf4ca106e853a1c398479a928e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda777b1585aec2e723c62cea962e526.png)
您最近一年使用:0次
2020-12-29更新
|
1550次组卷
|
5卷引用:内蒙古自治区赤峰市赤峰二中2021-2022学年高二上学期期末数学理科试题
内蒙古自治区赤峰市赤峰二中2021-2022学年高二上学期期末数学理科试题江西省新余市2020-2021学年高二下学期期末数学(理)试题广东省高州市2021届高三上学期第一次模拟数学试题(已下线)重难点 03 空间向量与立体几何-2021年高考数学(理)【热点·重点·难点】专练辽宁省凌源市2020-2021学年高三3月尖子生抽测数学试题
名校
4 . 如图,在正方体
中,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/a334f5fd-4f33-466d-b6c8-a48432213e50.png?resizew=132)
(1)求证:
平面
;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/a334f5fd-4f33-466d-b6c8-a48432213e50.png?resizew=132)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
您最近一年使用:0次
2020-12-04更新
|
413次组卷
|
8卷引用:内蒙古赤峰市红山区2020-2021学年高二上学期期末质量检测理科数学试题
20-21高一上·全国·课后作业
名校
解题方法
5 . 如图,四棱锥P﹣ABCD的底面ABCD为菱形,PB=PD,E,F分别为AB和PD的中点.
(2)求证:平面PBD⊥平面PAC.
(2)求证:平面PBD⊥平面PAC.
您最近一年使用:0次
2020-09-23更新
|
4840次组卷
|
15卷引用:内蒙古巴彦淖尔市临河区第三中学2021-2022学年高三(计算机班)上学期期末数学试题
内蒙古巴彦淖尔市临河区第三中学2021-2022学年高三(计算机班)上学期期末数学试题黑龙江省大庆市第二中学2020-2021学年高一下学期期末数学试题海南省琼海市嘉积中学2021-2022学年高一下学期期末数学试题湖南省郴州市2021-2022学年高一下学期期末数学试题湖南省长沙市宁乡市2021-2022学年高二下学期期末数学试题天津市南开区2022-2023学年高一下学期6月阶段性质量检测(期末)数学试题山西省阳高县第一中学校2022-2023学年高一下学期期末数学试题专题05 空间直线、平面的垂直-《期末真题分类汇编》(新高考专用)(已下线)专题04 空间中的平行、垂直关系-期末真题分类汇编(天津专用)(已下线)第08章+立体几何初步(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版)(已下线)第八章知识总结及测试-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)广东省雷州市第二中学2020-2021学年高二上学期期中数学试题陕西省安康中学,安康中学分校,高新中学等2021-2022学年高二上学期期中联考文科数学试题陕西省宝鸡市扶风县法门高中2023-2024学年高一下学期期中考试数学试卷宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期5月月考数学试题
解题方法
6 . 如图,
中,
,
是边长为1的正方形,平面
底面
,若
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2cce7fae-301b-400c-84fc-c75fc10bf9a9.png?resizew=180)
(1)求证:
底面
;
(2)求证:
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6321a96e7f0768394f6932a121adc84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2cce7fae-301b-400c-84fc-c75fc10bf9a9.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf60ad9db3411f35704fa88d86bfef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36148e5b0d89ba45bd98b91da00bf2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aad836ea6660232f48645cc775176a6.png)
您最近一年使用:0次
解题方法
7 . 已知四棱锥
,底面
是
,边长为
的菱形,又
底面
,且
,
,
分别为棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/ac0da8f0-b636-4a47-a75f-84fb88a5320a.png?resizew=179)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdf6426f0eaa95c31648895d35fe165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e2267c84394668eff2e9f5918de4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/ac0da8f0-b636-4a47-a75f-84fb88a5320a.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8ec2583c364c079a7b1bfb1e8fe0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
您最近一年使用:0次
解题方法
8 . 如图所示的几何体中,四边形
是正方形.四边形
是梯形
,
,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2020/8/18/2530428719104000/2541350020415488/STEM/946dc87c-4dbe-47e2-a00a-a30c37cee63a.png)
(1)求证:
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bce6eba5d07a34f24c5370c580ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db13e8affea90632f591077308119cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3025e649f4d4bc6bbda122f940cf8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c032261d2f887de100ed40e8fc676e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18177e13df82a638280a154aba6e45e.png)
![](https://img.xkw.com/dksih/QBM/2020/8/18/2530428719104000/2541350020415488/STEM/946dc87c-4dbe-47e2-a00a-a30c37cee63a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c0f6b53de48e0f7a09419886276ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ad3801636f311f226766d93859851e.png)
您最近一年使用:0次
2020-09-02更新
|
377次组卷
|
2卷引用:内蒙古赤峰市2019-2020学年下学期期末高二年级学年联考试卷(A)理科数学
名校
9 . 如图,长方体
的底面
是正方形,点
在棱
上,
.
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525089446600704/2528631114301440/STEM/f4ea3618ef804322a87c0071dfcd4c9c.png?resizew=157)
(1)证明:
平面
;
(2)若点
为棱
的中点,
.
①求四棱锥
的体积;
②求直线
与平面
所成角的正弦值.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0e0fdbd4c5be81d4566f230d21f39a.png)
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525089446600704/2528631114301440/STEM/f4ea3618ef804322a87c0071dfcd4c9c.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adf679c5b5063388202ee10d28ee8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
①求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e238bddad2ce99ad06214bf9d4eecc30.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becf2941e15d668d93ea6ed980afd0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
10 . 如图,四棱锥
中,
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525064058159104/2528358457024512/STEM/f1de6c9d-68f3-45ed-8a41-115512318c26.png)
(1)求证:
平面
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dd55b363934b4b89b381b985e22f39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc50067f63e524f638e2464bfa6ed73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba81f463e4471925ac08bfe8f63ba6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8daeebf7f1ad89d0dfdcad49a12d5e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a8bc0e66fd0bd01a8f0c807be31a5.png)
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525064058159104/2528358457024512/STEM/f1de6c9d-68f3-45ed-8a41-115512318c26.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d50356a01ae13936f1bd8efa94c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
您最近一年使用:0次
2020-08-15更新
|
421次组卷
|
3卷引用:内蒙古通辽市扎鲁特旗第一中学2019-2020学年高二第二学期期末考试数学(文科)试题
内蒙古通辽市扎鲁特旗第一中学2019-2020学年高二第二学期期末考试数学(文科)试题江苏省四校(徐州一中、兴化中学、致远中学、南京十三中)2020-2021学年高三上学期第三次适应性联考数学试题(已下线)江苏省如皋市2020-2021学年高一下学期期中模拟(二)数学试题