解题方法
1 . 如图在三棱台
中,
平面
,
,
,
.
(1)求点
到平面
的距离;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260ee90b4107dcdc5b2b0937c40e8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ba708880f5eb782acbf2c961c2494c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/23/c7cfdbb8-224d-49bc-9920-71c9906d7e26.png?resizew=146)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ead078d0c9a22439c512767bf3d4c7.png)
您最近一年使用:0次
解题方法
2 . 如图,在直三棱柱
中,
,
,
,
分别为
,
和
的中点,
为棱
上的一动点,且
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/3451fcd6-5c73-4a93-bd6d-78d0c8c54c88.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89955e0098755a46c7977fbf91e920ba.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0023280949eda97787964f0a9d41ed2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/3451fcd6-5c73-4a93-bd6d-78d0c8c54c88.png?resizew=152)
A.![]() |
B.三棱锥![]() |
C.![]() |
D.异面直线![]() ![]() ![]() |
您最近一年使用:0次
2023-02-03更新
|
1166次组卷
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6卷引用:浙江省浙里卷天下2023届高三一模数学试题
浙江省浙里卷天下2023届高三一模数学试题广东省江门市部分学校2023届高三下学期开学联考数学试题浙江省部分学校2022-2023学年高三上学期1月联考数学试题浙江省金太阳联盟2022-2023学年高三上学期1月期末联考数学试题(已下线)湖南省新高考教学教研联盟2023届高三下学期4月第二次联考数学试题变式题6-10山西省忻州市2023届高三一模数学试题
解题方法
3 . 如图,在三棱柱
中,
平面
,D,E分别为棱AB,
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/973d0791-ff5b-4568-854a-64067adb7da4.png?resizew=128)
(1)证明:
平面
;
(2)若三棱锥
的体积为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee631002406bf7468e534b647fc918a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/973d0791-ff5b-4568-854a-64067adb7da4.png?resizew=128)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7cd40c9d26ada55e07fa71a4b98be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf462eaaad82d6bc3b460385fd9f0de.png)
您最近一年使用:0次
2023-02-03更新
|
1461次组卷
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5卷引用:浙江省浙里卷天下2023届高三一模数学试题
名校
4 . 已知三棱锥
的底面
是正三角形,则下列各选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.若平面![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-06-18更新
|
638次组卷
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6卷引用:浙江省衢州市2021-2022学年高二下学期6月教学质量检测数学试题
浙江省衢州市2021-2022学年高二下学期6月教学质量检测数学试题广东省广州市海珠外国语实验中学2022-2023学年高二上学期期末数学试题广东省广州市海珠外国语实验中学2022-2023学年高二上学期期末数学试题(已下线)第一章 空间向量与立体几何(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)(已下线)第二章 立体几何中的计算 专题一 空间角 微点7 二面角大小的计算(二)【基础版】(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点2 空间向量基底法(二)【基础版】
解题方法
5 . 在矩形
中,
,
,点
为线段
上的中点,沿
将
翻折,使得
,点
在线段
上且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/15806d1c-89e7-4093-902c-bb5cb86c4cb8.png?resizew=204)
(1)证明:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101da161ae17652ccbe7d3f888762c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69509ad4786945359ce950ad284d0c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d669df6c391aa83150df5ae96c39d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/15806d1c-89e7-4093-902c-bb5cb86c4cb8.png?resizew=204)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e462c38951671d0dbbea78246da9f580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
6 . 如图,在三棱柱
中,
,D为BC的中点,平面
平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/58c2f1a7-4806-4472-bc64-7dae0faedcd6.png?resizew=159)
(1)证明:
;
(2)已知四边形
是边长为2的菱形,且
,问在线段
上是否存在点E,使得平面EAD与平面EAC的夹角的余弦值为
,若存在,求出CE的长度,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/58c2f1a7-4806-4472-bc64-7dae0faedcd6.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21478f83184c0f7577f8e24079abe381.png)
(2)已知四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
您最近一年使用:0次
2022-02-15更新
|
766次组卷
|
4卷引用:浙江省衢州市江山中学2023-2024学年高二上学期10月阶段性检测数学试题
名校
解题方法
7 . 长方体
,
,
,点
在长方体的侧面
上运动,
,则二面角
的平面角正切值的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbcdb9f641a2b3e06e0a01c79420667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-10更新
|
1332次组卷
|
10卷引用:浙江省衢州市2020-2021学年高二下学期期末数学试题
浙江省衢州市2020-2021学年高二下学期期末数学试题重庆市荣昌中学校2020-2021学年高二上学期十月月考数学试题(已下线)第一章 空间向量与立体几何(选拔卷)-【单元测试】2021-2022学年高二数学尖子生选拔卷(人教A版2019选择性必修第一册)福建省福州市长乐第一中学2021-2022学年高二10月月考数学试题(已下线)第1.6讲 用空间向量研究距离、夹角问题-2021-2022学年高二数学链接教材精准变式练(人教A版2019选择性必修第一册)(已下线)专题卷01 空间向量与立体几何— 章节重难点突破卷-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)1.4空间向量的应用(课前预习+课堂探究)-2021-2022学年高二数学课堂精选(人教A版2019选择性必修第一册)(已下线)解密15 空间向量与立体几何 (分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)(已下线)解密15 空间向量与立体几何 (讲义)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)(已下线)第06讲 向量法求空间角(含探索性问题) (讲)-3
解题方法
8 . 如图,在梯形
中,
,
,四边形
为矩形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747941521244160/2782500585103360/STEM/a787e6a0-4c4b-4513-9ab0-b24fad78fa0b.png?resizew=226)
(Ⅰ)求证:
;
(Ⅱ)若
,
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747941521244160/2782500585103360/STEM/a787e6a0-4c4b-4513-9ab0-b24fad78fa0b.png?resizew=226)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c79c4d655d22f6b3e9826adc6df810.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ea9d92e5c258a50af1e461c7388894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bc25a55fe974bc2942e4bb7cde9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
9 . 如图,在三棱锥P—ABC中,PA⊥平面ABC,AC⊥BC,D为PC中点,E为AD中点,PA=AC=2,BC=1.
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503776547430400/2503829992464384/STEM/aa082dc0-4db2-4172-97f7-67eb54d64919.png?resizew=210)
(1)求证:AD⊥平面PBC:
(2)求PE与平面ABD所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2020/7/11/2503776547430400/2503829992464384/STEM/aa082dc0-4db2-4172-97f7-67eb54d64919.png?resizew=210)
(1)求证:AD⊥平面PBC:
(2)求PE与平面ABD所成角的正弦值.
您最近一年使用:0次
2020-07-11更新
|
383次组卷
|
3卷引用:浙江省衢州市2019-2020学年高二下学期6月期末教学质量检测数学试题
浙江省衢州市2019-2020学年高二下学期6月期末教学质量检测数学试题(已下线)专题09 法向量秒求-2021年高考数学二轮复习解题技巧汇总(新高考地区专用)安徽省滁州市定远县育才学校2022-2023学年高二上学期第一次月考数学试题
10 . 四棱锥
中,
,底面
为等腰梯形,
,
,
为线段
的中点,
.
![](https://img.xkw.com/dksih/QBM/2020/8/16/2528949163974656/2529126425985024/STEM/cd031c7b-9691-4b0a-8ff9-ce0479ef92d6.png)
(1)证明:
平面
;
(2)若
,求直线
与平面
所成角正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42de572d68ded125eccccc512c4fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6abed28fd7b66cc392d16edc057d834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5148e7fc64ac3fed107192236f8e129d.png)
![](https://img.xkw.com/dksih/QBM/2020/8/16/2528949163974656/2529126425985024/STEM/cd031c7b-9691-4b0a-8ff9-ce0479ef92d6.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
您最近一年使用:0次
2020-08-16更新
|
387次组卷
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5卷引用:浙江省衢州四校2019-2020学年高二上学期期中数学试题
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