名校
解题方法
1 . 如图,在四棱锥P—ABCD中,
平面ABCD,底面ABCD是直角梯形,其中AD∥BC,
,E为棱BC上的点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6d9a407beaf65ad3f311971eeba30.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987202054963200/2987907091619840/STEM/52ce0c21-c483-43bb-9c04-ca4251733964.png?resizew=196)
(1)求证:DE⊥平面
;
(2)求二面角
的余弦值;
(3)设Q为棱CP上的点(不与C、P重合),且直线QE与平面PAC所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6bfc40d98a735f6f717bcced546dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6d9a407beaf65ad3f311971eeba30.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987202054963200/2987907091619840/STEM/52ce0c21-c483-43bb-9c04-ca4251733964.png?resizew=196)
(1)求证:DE⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07edbbae5955968df5486d73e1bf7fc3.png)
(3)设Q为棱CP上的点(不与C、P重合),且直线QE与平面PAC所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf8af35735950780f8c72f1268bcf52.png)
您最近一年使用:0次
2022-05-26更新
|
1257次组卷
|
15卷引用:2020届天津市南开中学高三第一学期数学统练八试题
2020届天津市南开中学高三第一学期数学统练八试题2020届天津市耀华中学高三数学上学期第一次月考数学试题天津市宁河区芦台第一中学2020届高考二模数学试题(已下线)专题17 立体几何(解答题)-2020年高考数学母题题源解密(天津专版)(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)天津市八校2020-2021学年高三上学期期中联考数学试题天津市咸水沽第一中学2021-2022学年高三上学期第二次月考数学试题天津北京师范大学静海附属学校2021-2022学年高二上学期第一次月考数学试题天津市宝坻区大口屯高中2021-2022学年高三上学期结课考试数学试题天津市市区重点中学2022届高三下学期三模数学试题天津市外国语大学附属外国语学校2022-2023学年高三上学期第一次月考数学试题天津外国语大学附属外国语学校2020-2021学年高三上学期结课检测数学试题河北省石家庄市十八中2022-2023学年高二上学期第一次月考数学试题重庆市兼善中学2022-2023学年高二上学期第二次阶段考数学试题(已下线)专题8-2 立体几何中的角和距离问题(含探索性问题)-1
名校
解题方法
2 . 如图,在直三棱柱
中,已知
,
,
为棱
的中点,
为线段
的中点.
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/85705492-062d-4f18-ace9-43ad8c44e64d.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68810418922056adb838462f125dc403.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128bcefc524d180d611d6b6919eaca27.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在多面体ABCDEF中,AE⊥平面ABCD,AEFC是平行四边形,且AD∥BC,AB⊥AD,AD=AE=2,AB=BC=1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/9b2817b6-179b-4af9-8c16-bd51c15aab53.png?resizew=180)
(1)求证:CD⊥EF;
(2)求平面ADE与平面DEB夹角的余弦值;
(3)若点P在棱CF上,直线PB与平面BDE所成角的正弦值为
,求线段CP的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/9b2817b6-179b-4af9-8c16-bd51c15aab53.png?resizew=180)
(1)求证:CD⊥EF;
(2)求平面ADE与平面DEB夹角的余弦值;
(3)若点P在棱CF上,直线PB与平面BDE所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
您最近一年使用:0次
2021-12-25更新
|
685次组卷
|
4卷引用:天津市南开中学2021-2022学年高三上学期第二次统练数学试题
天津市南开中学2021-2022学年高三上学期第二次统练数学试题江西省赣州市教育发展联盟2021-2022学年高二上学期第7次联考高二数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)考点36 利用空间向量法解决立体几何的综合问题【理】-备战2022年高考数学典型试题解读与变式
名校
解题方法
4 . 四棱锥
中,
面
,
,
,
是
的中点,
在线段
上,且满足
.
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)在线段
上是否存在点
,使得
与平面
所成角的余弦值是
,若存在,求出
的长;若不存在,请说明理由.
![](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/600e47e5295f977e400f025bfd9eda98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63181e1512d862f309439a7408bef51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbae68020a497f0c021bea162bcebaf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/29/39632c8b-a5e4-44c8-a065-eefc2e57b84f.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7440b41636c761b0910639e310ff7dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60aa084359c6919653fdcbd2f4c26ede.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632917e61f4208959686d118c7f19231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee72fd8a5a52d08a4fddcf0830a8e103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
您最近一年使用:0次
2023-01-31更新
|
1176次组卷
|
24卷引用:天津市南开大学附中2020-2021学年高三上学期第二次月考数学试题
天津市南开大学附中2020-2021学年高三上学期第二次月考数学试题天津市南开中学2023届高三统练24数学试题【全国校级联考】滨海新区七所重点学校2018届高三毕业班联考数学(理)试题天津市滨海新区七所重点学校2017-2018学年高三毕业班联考数学(理)试题天津市实验中学2019-2020学年高三上学期第二次阶段考试数学试题黑龙江省哈尔滨师范大学青冈实验中学校2020-2021学年高二10月月考数学(理)试题天津市实验中学2019-2020学年高二(上)第二次段考数学试题江西省赣县第三中学2020-2021学年高二12月月考数学(理)试题天津市第四中学2020-2021学年高三上学期第三次月考数学试题湖南省长沙市第一中学2020-2021学年高一下学期第二次阶段性检测数学试题黑龙江省鹤岗市第一中学2021-2022学年高二上学期开学考试数学试题(已下线)第04讲 空间向量的应用(教师版)-【帮课堂】北京市西城区北京师范大学第二附属中学2021-2022学年高二上学期期中数学试题四川省资阳中学校2021-2022学年高二上学期期中考试数学(理)试题黑龙江省七台河市勃利县高级中学2021-2022学年高二上学期9月月考数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)北京市北京师范大学第二附属中学2021-2022学年高二上学期期中数学试题北京市师大二附中2020-2021学年高二上学期期中数学试题北京市首都师范大学附属中学昌平学校2022-2023学年高二上学期期中考试数学试题北京市首都师范大学附属中学2022-2023学年高二上学期期中考试数学试题天津市咸水沽第一中学2021届高三下学期模拟检测(四)数学试题(已下线)天津市耀华中学2024届高三上学期第一次月考数学试题变式题16-20天津市滨海新区塘沽紫云中学2024届高三上学期期末模拟数学试题(六)(已下线)单元高难问题01探索性问题(各大名校30题专项训练)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)
名校
解题方法
5 . 如图,在三棱锥
中,平面
平面
,
,
,
分别为
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848859527716864/2849639249453056/STEM/bf47cd72-f084-48f7-a735-fe26c9b1dff8.png)
(1)求点
到直线
的距离
(2)求平面
与平面
夹角的余弦值
(3)已知
是平面
内一点,点
为
中点,且
平面
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ed20e68b1df31a3d7dfd31b427bef.png)
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848859527716864/2849639249453056/STEM/bf47cd72-f084-48f7-a735-fe26c9b1dff8.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2021-11-12更新
|
411次组卷
|
3卷引用:天津市第二十五中学2021-2022学年高二上学期阶段检测数学试题
名校
6 . 如图,已知多面体
,
,
,
均垂直于平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/6ba1b967-69e7-43c9-b46a-857bb08be045.png?resizew=138)
(1)证明:
平面
;
(2)求平面
与平面
所成角的正弦值;
(3)线段
上是否存在一点
,使直线
与平面
所成的角的正弦值为
,若存在,求
的长,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d17d14819681c455a91d7678742368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a2749f3f4224a1753bcbe2e13b88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c709354113697ec9c577c7b2449a12f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/6ba1b967-69e7-43c9-b46a-857bb08be045.png?resizew=138)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd92f594c348f7a956607f7b381cc22a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2021-11-03更新
|
705次组卷
|
4卷引用:天津市南开区2021-2022学年高三上学期期中数学试题
天津市南开区2021-2022学年高三上学期期中数学试题(已下线)第35讲 利用传统方法解决立体几何中的角度与距离问题-2022年新高考数学二轮专题突破精练(已下线)考点34 二面角【理】-备战2022年高考数学典型试题解读与变式天津市静海区第一中学2021-2022学年高三上学期第四次阶段检测数学试题
名校
7 . 如图,已知三棱柱
中,侧棱与底面垂直,且
,
,
、
分别是
、
的中点,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712391979089920/2714010239172608/STEM/2733a15f-477f-4d2f-8714-5f9d6f0dfdca.png?resizew=244)
(1)求证:不论
取何值,总有
;
(2)当
时,求平面
与平面
所成锐二面角的余弦值;
(3)当直线
与平面
所成角的正弦值为
时,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7baf1a8607125e0e5220b5baf03263.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712391979089920/2714010239172608/STEM/2733a15f-477f-4d2f-8714-5f9d6f0dfdca.png?resizew=244)
(1)求证:不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ece75fe9b8555909be5a00d2b7af0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cb57b942813635ef4e4c3bea67928f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
解题方法
8 . 如图,在四棱柱
中,侧棱
底面
,
,
,
,
,且点
和
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801377753874432/2802270999470080/STEM/3ddd4bca-c9d3-4bd7-b796-bd1a7e3d729b.png?resizew=323)
(1)求证:
平面
;
(2)求二面角
的正弦值;
(3)求点
到平面
的距离;
(4)设
为棱
上的点,若直线
和平面
所成角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c2888dad200ebe6cbc60b7a680ad6e.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/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801377753874432/2802270999470080/STEM/3ddd4bca-c9d3-4bd7-b796-bd1a7e3d729b.png?resizew=323)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88595db9e3a4bf66275eae21fe0238e7.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefd8229243bcbee5ac197740e6c66ab.png)
(4)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
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名校
9 . 如图,四棱锥P - ABCD的底面是边长为2的正方形,侧面PCD⊥底面ABCD,且PC= PD=2,M,N分别为棱PC,AD的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878718720335872/2887219036266496/STEM/478c1da779504f82b13cd910c7158747.png?resizew=201)
(1)求证∶ BC⊥PD;
(2)求异面直线BM与PN所成角的余弦值;
(3)求点N到平面MBD的距离.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878718720335872/2887219036266496/STEM/478c1da779504f82b13cd910c7158747.png?resizew=201)
(1)求证∶ BC⊥PD;
(2)求异面直线BM与PN所成角的余弦值;
(3)求点N到平面MBD的距离.
您最近一年使用:0次
2022-01-04更新
|
664次组卷
|
3卷引用:天津市南开区崇化中学2019-2020学年高二上学期期中数学试题
解题方法
10 . 如图所示,四棱锥
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/4/2/2691268925587456/2691666054930432/STEM/2357e084ba5249719cf76ba27668fbac.png?resizew=165)
(1)求
与平面
所成角的正弦值;
(2)求二面角
的正弦值;
(3)设
为
上一点,且
,若
平面
,求
的长.
![](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/fb886ce5fa68b1bafeed307589576348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d40978fbe52316daaaa6bdbb403fea0.png)
![](https://img.xkw.com/dksih/QBM/2021/4/2/2691268925587456/2691666054930432/STEM/2357e084ba5249719cf76ba27668fbac.png?resizew=165)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4eebde0291ae62d02a498b56358ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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