1 . 已知动圆
经过定点
,且与圆
:
内切.
(1)求动圆圆心
的轨迹
的方程;
(2)设轨迹
与
轴从左到右的交点为
,
,点
为轨迹
上异于
,
的动点,设
交直线
于点
,连接
交轨迹
于点
,直线
,
的斜率分别为
,
.
①求证:
为定值;
②证明:直线
经过
轴上的定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866502435d9ea08c6d3a5e304a8986c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811dd726ed27d28ad5a8e83fbb20ed6.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef79861421b414b455a090a3ef04fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b51a4949896526cfc3c076ea8dec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a51e6728d354cc1c3d32e2d4368d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d727db2181aca4e8a6455d10cfe28.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6b1769274eee3ce2896cb3513d50f8.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-01-11更新
|
630次组卷
|
11卷引用:广东省梅州市2023届高三一模数学试题
名校
解题方法
2 . 已知双曲线
的焦距为
,点
在
上.
(1)求
的方程;
(2)直线
与
的右支交于
,
两点,点
与点
关于
轴对称,点
在
轴上的投影为点
.
(ⅰ)求
的取值范围;
(ⅱ)求证:直线
过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0c551cfc411bdb73d2d94e72a274ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51698f7095e795d4f0527b986ac1db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a771f2e80c8a29ed2ebd76498b0f49.png)
(ⅱ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2024-05-13更新
|
1211次组卷
|
3卷引用:广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题
名校
解题方法
3 . 如图,在五面体
中,底面
为正方形,
.
;
(2)若
为
的中点,
为
的中点,
,再从条件①、条件②这两个条件中选择一个作为已知,求直线
与平面
所成角的正弦值.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答计分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410666db488a1c79eca80e51f4278e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666734423f1818d76a74f171b7420b68.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6e498f70417224e1f3cf28c5b88df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1976e2a7028cacd09bd7a83ca89bd23.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc5df62e8ac9c74a46462519b95479a.png)
注:如果选择条件①和条件②分别解答,按第一个解答计分
您最近一年使用:0次
2024-04-08更新
|
1989次组卷
|
6卷引用:广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题
广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题北京市东城区2023-2024学年高三下学期综合练习(一)(一模)数学试题(已下线)模块3 第6套 全真模拟篇(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)江苏省南京航空航天大学苏州附属中学2023-2024学年高三下学期二模阳光测试数学试题(已下线)模块五 专题1 全真基础模拟1(苏教版高二期中研习)
名校
解题方法
4 . 如图所示,圆锥的高
,底面圆
的半径为
,延长直径
到点
,使得
,分别过点
、
作底面圆
的切线,两切线相交于点
,点
是切线
与圆
的切点.
平面
;
(2)若平面
与平面
所成锐二面角的余弦值为
,求该圆锥的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0819cd060cdfb72896f379db29a4724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c76a0cbea833ae927c2f05602a965ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22583ac400216f5aa56a84284efe4b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15b63176f43bc7a0654d0f6f45e7429.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
5 . 已知三棱柱
中,
,
,且
,
,侧面
底面
,
是
的中点.
平面
;
(2)在棱
上是否存在点
,使得
与平面
的所成角为60°.如果存在,请求出
;如果不存在,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/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d960679bc2aa81f9100bcced84dbc20e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e238b2757353026133bbe495645e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/d24243a33f3ad70cec7d4e15297d11e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb87785b2842459c59b2571aac7374b.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a934b31dd77112ee7be67ecaf46fcad6.png)
您最近一年使用:0次
名校
6 . 如图,在四棱锥
中,
平面
,底面
为菱形,
分别为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ccd2c4b9ef8b0b42ab92635adf7e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a62c799deed7df3eecd462d2f88882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2023-10-10更新
|
756次组卷
|
23卷引用:广东省梅州市大埔县虎山中学2022-2023学年高三上学期第三次教学质量检测数学试题
广东省梅州市大埔县虎山中学2022-2023学年高三上学期第三次教学质量检测数学试题湖南省永州市第一中学2022-2023学年高三上学期入学考试数学试题(已下线)第10讲 第七章 立体几何与空间向量(综合测试)湖南省长沙市明德中学2022-2023学年高三上学期入学考试数学试题福建省三明第一中学2023届高三上学期第二次月考数学试题广东省深圳市福田区外国语高级中学2023届高三上学期第二次调研数学试题广东省普宁市华美实验学校2023届高三上学期第二次月考数学试题上海市格致中学2023届高三下学期3月阶段性测试数学试题江苏省南通市通州高级中学2022-2023学年高三上学期第一次阶段性测试数学试题福建省莆田锦江中学2023-2024学年高三上学期期中考试数学试题贵州省毕节市2021-2022学年高二下学期联合考试数学(理)试题内蒙古自治区通辽市霍林郭勒市2021-2022学年高二下学期期末数学理科试题湖南省衡阳市祁东县2021-2022学年高二下学期期末数学试题第一章 空间向量与立体几何(A卷·知识通关练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教A版2019)江苏省南通市海安高级中学2022-2023学年高二上学期第一次月考数学试题(已下线)第一章 空间向量与立体几何(A卷·知识通关练)(2)安徽省安庆市外国语学校2022-2023学年高二上学期第一次月考数学试题黑龙江省齐齐哈尔市第八中学校2022-2023学年高二上学期期中数学试题河南省中原名校联考2023-2024学年高二上学期9月月考数学试题河南省开封市五县联考2023-2024学年高二上学期第一次月考数学试题福建省厦门市厦门大学附属科技中学2023-2024学年高二上学期10月月考数学试题云南省昆明市第二十四中学2023-2024学年高二上学期10月月考数学试题(已下线)模块一 专题2 利用空间向量解决立体几何问题 (讲)2 期末终极研习室(2023-2024学年第一学期)高二人教A版
7 . 如图①,在
中,B为直角,AB=BC=6,EF∥BC,AE=2,沿EF将
折起,使
,得到如图②的几何体,点D在线段AC上.
(1)求证:平面
平面ABC;
(2)若
平面BDF,求直线AF与平面BDF所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4215ae359227ff75071903accff4feba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/22/8d130baf-b932-4776-90f5-25ec450cba60.png?resizew=286)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
您最近一年使用:0次
2023-06-21更新
|
724次组卷
|
8卷引用:广东省梅州市大埔县虎山中学2023届高三高考热身数学试题
广东省梅州市大埔县虎山中学2023届高三高考热身数学试题山东省临沂市(二模)、枣庄市(三调)2020届高三临考演练考试数学试题(已下线)专题九 立体几何与空间向量-山东省2020二模汇编江苏省如皋市部分学校2021-2022学年高三上学期8月调研数学试题(已下线)专题03 立体几何大题江苏省盐城市响水县第二中学2022-2023学年高二下学期期中数学试题(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)第11讲 第一章 空间向量与立体几何 章末题型大总结(1)
名校
解题方法
8 . 如图所示,四边形ABCD为圆柱ST的轴截面,点Р为圆弧BC上一点(点P异于B,C).
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
,
(
),且二面角
的余弦值为
,求
的值.
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8798f21caf1819d47db778d23fa57b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2590902f4edd2fa6b233ef54a31862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d80c787eefc6da2a49d25d2caeaa5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-01-12更新
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1137次组卷
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5卷引用:广东省梅州市梅县东山中学2024届高三上学期期末数学试题
名校
9 . 如图,已知平行六面体
中,所有棱长均为2,底面
是正方形,侧面
是矩形,点
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/af78e578-3055-4743-bed3-33464b47857d.png?resizew=164)
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c8a72acdef14452a6c62f2a60a15fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/af78e578-3055-4743-bed3-33464b47857d.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddbb0422a136f45653c8c369f2d75fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955e030d649a3c7885071b4bf849993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5082fa0f36a008dc2838146ea2bf2e1b.png)
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2023-11-01更新
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533次组卷
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3卷引用:广东省梅州市蕉岭县蓝坊中学2023-2024学年高三上学期第三次质检数学试题
10 . 如图,在边长为4的正三角形
中,
为边
的中点,过
作
于
.把
沿
翻折至
的位置,连接
、
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/4665f60d-7144-48d8-8587-b8b3d3432200.png?resizew=207)
(1)
为边
的一点,若
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
平面
;
(2)当四面体
的体积取得最大值时,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b84c9d873289f99d8eb733d12899280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/4665f60d-7144-48d8-8587-b8b3d3432200.png?resizew=207)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34656afc8db21ef12e0fd103849dfc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67be899bc131ec1b9921ae9787c40d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)当四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e38e5ff94bd213dbd16452cc515a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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