名校
解题方法
1 . 如图,在底面为菱形的直四棱柱
中,
,
分别是
的中点.
;
(2)求平面
与平面
所成夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709a9e8bdb91467826fdf8ee31ac63c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4cf79ee8726310da8faf61f70cfa682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fe6d64ca3dd8568a059d4b867d00ca.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-03-12更新
|
1329次组卷
|
5卷引用:上海市宜川中学2024届高三下学期2月开学考试数学试题
上海市宜川中学2024届高三下学期2月开学考试数学试题山东省泰安市2024届高三下学期一轮检测数学试题(已下线)信息必刷卷04(上海专用)湖北省天门市天门中学2023-2024学年高二下学期3月月考数学试题(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
名校
解题方法
2 . 如图,多面体
中,四边形
为矩形,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/3323c5b9-8334-4c90-9872-e4e1a6323f5f.png?resizew=150)
(1)求证:
⊥
;
(2)求直线
与平面
所成角的正弦值;
(3)求出
的值,使得
,且
到平面
距离为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019c0405370c673e37b46c066eba839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d40d5cb59338d3cb1dd504bb12d107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6870026fcfde41e27f9a7871fdae95d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f1e80e44f107af592fc8fd96419ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56512504254ab7f574a717dd6830fb33.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/3323c5b9-8334-4c90-9872-e4e1a6323f5f.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00d4825584cf2a3f381de72c179e22.png)
(3)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e347ebb3d68d0ae72f05fa5d23675db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
名校
3 . 如图,在四棱台
中,底面
为矩形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
;
(2)求直线
和平面
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/384ffa4e596b6c7b8e270217a47f7227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6503add5811927fc11d86f2174f79f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e076e68ef7bab94a6aba990f83159f51.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2022-02-04更新
|
1520次组卷
|
3卷引用:上海市实验学校2024届高三上学期暑假阶段反馈数学试题
上海市实验学校2024届高三上学期暑假阶段反馈数学试题浙江省绍兴市2021-2022学年高三上学期期末数学试题(已下线)技巧03 解答题解法与技巧(练)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(浙江专用)》
名校
4 . 已知四棱锥
中,
平面
,且
,底面
是边长为b的菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/26668076-05c9-4c41-9de9-7dbf48f53120.png?resizew=217)
(1)求证:平面
平面
;
(2)设
与
交于点
为
中点,若二面角
的正切值是
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00803e67a5d417a9a4dc00277fca778b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/26668076-05c9-4c41-9de9-7dbf48f53120.png?resizew=217)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef19f98e86ae7504671413780b3b1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa8be8dc00840d3544f3b7264f83312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e15186cf03e17275602581a1da03fe.png)
您最近一年使用:0次
2021-09-13更新
|
1159次组卷
|
3卷引用:山东省师范大学附属中学2021-2022学年高三上学期开学考试数学试题
山东省师范大学附属中学2021-2022学年高三上学期开学考试数学试题广东省汕头市澄海中学2022届高三上学期第一学段考试数学试题(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
解题方法
5 . 如图,四棱锥
的底面为矩形,
底面
,设平面
与平面
的交线为m.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9a6cc04d-e30c-4f87-904b-c268d0c080ef.png?resizew=142)
(1)证明:
,且
平面
;
(2)已知
,R为m上的点求
与平面
所成角的余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9a6cc04d-e30c-4f87-904b-c268d0c080ef.png?resizew=142)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcd6b9e470aab93e77dab8ce476eb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f979a27d3a09a17445561091e6655eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5da631296d53a08d56fb5f9bec2376c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517d67c30a82da664d5663a401ced466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511bd2adf8e8614c7bba2a1580c7044.png)
您最近一年使用:0次
名校
6 . 如图在三棱锥P-ABC中,平面PAB⊥平面PBC,PB⊥BC,PD=DB=BC=AB=AD=2.
![](https://img.xkw.com/dksih/QBM/2021/9/3/2800036107902976/2801395416547328/STEM/bc8e1bc7-54a6-4ea9-8ad0-2e47501d2c75.png?resizew=198)
(1)证明:PA⊥平面ABC;
(2)求二面角B-AD-C的余弦值.
![](https://img.xkw.com/dksih/QBM/2021/9/3/2800036107902976/2801395416547328/STEM/bc8e1bc7-54a6-4ea9-8ad0-2e47501d2c75.png?resizew=198)
(1)证明:PA⊥平面ABC;
(2)求二面角B-AD-C的余弦值.
您最近一年使用:0次
2021-09-05更新
|
1546次组卷
|
4卷引用:安徽省名校联盟2021-2022学年高三上学期开学考试理科数学试题
安徽省名校联盟2021-2022学年高三上学期开学考试理科数学试题(已下线)2021年全国高考甲卷数学(理)试题变式题16-20题(已下线)2021年全国高考甲卷数学(理)试题变式题16-20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
名校
7 . 如图,在四棱锥
中,
平面
,底面
是直角梯形,其中
,
,
,
,E为棱
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/539de07f-0b4b-4cc1-9bcd-10da86d0f8a4.png?resizew=154)
(1)若F为棱
的中点,求证:
平面
;
(2)(i)求证
平面
;
(ii)设Q为棱
上的点(不与C,P重合),且直线
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfb2735e1683a6ae86b5b97a0032e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41744ec71119e7264ef9673a35805a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/539de07f-0b4b-4cc1-9bcd-10da86d0f8a4.png?resizew=154)
(1)若F为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)(i)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(ii)设Q为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2942447b6af4f2749668439d5ee03a7.png)
您最近一年使用:0次
2021-04-11更新
|
1103次组卷
|
4卷引用:天津市耀华中学2022届高三暑假线上调研数学试题
天津市耀华中学2022届高三暑假线上调研数学试题(已下线)一轮复习大题专练50—立体几何(线面角2)—2022届高三数学一轮复习北京市清华大学附属中学2020-2021学年高二上学期期末考试数学试题(已下线)专题02 空间向量与立体几何的典型题(二)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)
名校
8 . 如图,在三棱柱
中,
是边长为2的等边三角形,平面
平面
,四边形
为菱形,
,
与
相交于点D.
(1)求证:
.
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5f9ef971747d2d5bbc5823797a7a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140088b0cb73812aa9d523c44559298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a252001e9b7edcba240973a32ab3fb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/e8ee0cea-3dd2-45dc-9889-74bf5ac30626.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d57d82c046d22a1484e1c23ddbc9ee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
您最近一年使用:0次
2020-09-26更新
|
811次组卷
|
8卷引用:安徽省皖南八校2020-2021学年高三上学期摸底联考理科数学试题
安徽省皖南八校2020-2021学年高三上学期摸底联考理科数学试题(已下线)2021届普通高等学校招生全国统一考试数学考向卷(七)(已下线)专题19 立体几何综合-2020年高考数学母题题源全揭秘(浙江专版)内蒙古赤峰二中2020-2021学年高二上学期第二次月考数学(理)试题辽宁省凌源市2020-2021学年下学期高二尖子生抽测数学试题云南省曲靖市会泽县茚旺高级中学2020-2021学年高二春季6月月考数学(理)试题陕西省榆林市绥德中学2020-2021学年高二下学期6月质量检测理科数学试题云南省临沧市民族中学-2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 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/editorImg/2022/11/30/1aec0e7a-1bdf-4ff6-915c-6ba733ac01a9.png?resizew=170)
(1)求证:不论
取何值,总有
;
(2)当
时,求平面
与平面
所成二面角的余弦值.
![](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/666b6c488afe7142df3da04d0ef573cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/1aec0e7a-1bdf-4ff6-915c-6ba733ac01a9.png?resizew=170)
(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/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2020-08-05更新
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923次组卷
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11卷引用:河南省郑州市第一中学2020-2021学年高三上学期开学测试数学(理)
河南省郑州市第一中学2020-2021学年高三上学期开学测试数学(理)山西省实验中学2019-2020学年高三下学期3月开学摸底数学(理)试题四川省宜宾市叙州区第二中学校2020届高三第一次高考适应性考试数学(理)试题(已下线)专题04 立体几何——2020年高考真题和模拟题理科数学分项汇编(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)(已下线)专题18 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅰ专版)(已下线)专题04 空间角——2020年高考数学母题题源解密(山东、海南专版)湖南师大附中2020-2021学年高三上学期月考(四)数学试题(已下线)考点29 空间向量解决空间直线、平面位置关系-备战2021年新高考数学一轮复习考点一遍过四川省泸州市泸县2021-2022学年高三上学期期末数学理科试题(已下线)第02讲 空间向量的坐标表示-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)
名校
解题方法
10 . 直三棱柱
中,
,
,已知P是
的中点,Q是AC的中点,则异面直线
与PC所成角的余弦值为( )
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc74956a4f7adc5e7b057d2a0c6f5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab3d7e6077fe7ec725a5637c8bdfee1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-04-13更新
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2卷引用:山西省大同市第一中学2019-2020学年高三下学期2月网上月考(开学)数学(文)试题