名校
1 . 如图1,在边长为4的菱形
中,
,
于点
,将
沿
折起到
的位置,使
,如图2.
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379930112/STEM/a99ea2a0befd4d92b37fcaf4c90b89f4.png?resizew=417)
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)判断在线段
上是否存在一点
,使平面
平面
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460edcced5597615113c0fdc95b1dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f07107087ce4abdfa5fc68fe6fb62f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967bd1d8bd38f6be7931eef41db106.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572201374056448/1572201379930112/STEM/a99ea2a0befd4d92b37fcaf4c90b89f4.png?resizew=417)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a981cb7611787abb2df1e900915759.png)
(3)判断在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339128336cb6905dc8537e58f55ad3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14d78cfdef4aa7d877607e7fc35b3e3.png)
您最近一年使用:0次
2016-12-03更新
|
3581次组卷
|
11卷引用:2015届北京市西城区高三二模理科数学试卷
2015届北京市西城区高三二模理科数学试卷2016届河北省衡水中学高三下学期二调考试理科数学试卷2017届河北省衡水中学高三下学期第四周周测数学(理)试卷2017届河北省衡水中学高三下学期第四周周测数学(理)试卷(已下线)《高频考点解密》—解密16 空间向量与立体几何【全国百强校】天津市南开中学2019届高三上第二次月考数学试题(理科)河北省衡水中学2020届高三下学期第二次调研数学(理)试题河北省衡水中学2020届高三高考数学(理科)二调试题(已下线)解密15 空间向量与立体几何 (讲义)-【高频考点解密】2021年高考数学(理)二轮复习讲义+分层训练2017届河北省衡水中学高三下学期第四周周测数学(理)试卷陕西省安康中学2023-2024学年高二上学期10月月考数学试题
13-14高三·河南·开学考试
名校
解题方法
2 . 如图,四棱锥
中,底面
为菱形,
,Q是
的中点.
(1)若
,求证:平面
平面
;
(2)若平面
平面
,且
,点M在线段
上,试确定点M的位置,使二面角
的大小为
,并求出
的值.
![](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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845b8505cb7b7b8df5753f52a4e00462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931bbffda5e872703c9947eccc47ede2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a773fe6d12311dc321198697eb528ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519ba613bf121a2c1bc28c948266d74.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/5b4a34af-fa70-407e-a58b-3f4b0010ddf6.png?resizew=157)
您最近一年使用:0次
2016-12-03更新
|
1504次组卷
|
4卷引用:【全国百强校】北京东城北京二中2018届高三上学期期中考试数学(理)试题
【全国百强校】北京东城北京二中2018届高三上学期期中考试数学(理)试题(已下线)2015届河南省顶级名校高三入学定位考试理科数学试卷宁夏石嘴山市第三中学2017届高考一模数学(理)试题河南省信阳高级中学2017-2018学年高二4月月考数学(理)试题
2014·北京房山·一模
名校
3 . 如图,三棱柱
中,
平面
,
,
,
,以
,
为邻边作平行四边形
,连接
和
.
![](https://img.xkw.com/dksih/QBM/2014/5/12/1571712601071616/1571712607068160/STEM/625373d6-e844-43c7-a40f-acb2883d026f.png?resizew=193)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值;
(Ⅲ)线段
上是否存在点
,使平面
与平面
垂直?若存在,求出
的长;若不存在,说明理由.
![](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/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://img.xkw.com/dksih/QBM/2014/5/12/1571712601071616/1571712607068160/STEM/625373d6-e844-43c7-a40f-acb2883d026f.png?resizew=193)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ac809549102844f24d73a5bfdf2464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
(Ⅲ)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee076fe7dbca5616c4e8a6869a355f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2016-12-03更新
|
5895次组卷
|
3卷引用:2014届北京市房山区4月高三一模理科数学试卷
12-13高一上·北京·期末
解题方法
4 . 在四棱锥
中,底面
是直角梯形,
,
,
,平面
平面
.
(1)求证:
平面
;
(2)求平面
和平面
所成二面角(小于
)的大小;
(3)在棱
上是否存在点
使得
平面
?若存在,求
的值;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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0073c8e806d0399a6983e163f0fd176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ba22238cdff318a4bd9d4d746b3229.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b505e0df1131e3a93fc81d13f6e224e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/fa4fd412-897c-4621-b148-dc248d6cc7a6.png?resizew=135)
您最近一年使用:0次
2016-12-02更新
|
651次组卷
|
5卷引用:2011-2012学年北京市海淀区高三上学期期末考试理科数学
(已下线)2011-2012学年北京市海淀区高三上学期期末考试理科数学北京西城回民中学2018届高三上期中数学(理)试题北京市东城区2018届高三上学期期中考试数学试题(已下线)2011-2012学年北京市育园中学高一第一学期期末考试数学(已下线)2013届天津市天津一中高三第三次月考理科数学试卷
5 . 如图,已知四棱锥
的底面ABCD为正方形,
平面ABCD,E、F分别是BC,PC的中点,
,.
(1)求证:
平面
;
(2)求二面角
的大小.
![](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/bb35df1518ffc12d0ed7146f4111bcad.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40df8e474334faad849abb7cc6bbd12c.png)
![](https://img.xkw.com/dksih/QBM/2012/7/2/1570909508829184/1570909514047488/STEM/d44eba5542274873ae005e779241dfc0.png?resizew=189)
您最近一年使用:0次
2016-12-01更新
|
1744次组卷
|
11卷引用:2020届北京市怀柔区高三一模数学试题
2020届北京市怀柔区高三一模数学试题2020届北京怀柔区高三下学期适应性练习数学试题(已下线)专题16 立体几何-2020年高考数学母题题源解密(北京专版)(已下线)2012届上海市崇明县高三高考模拟考试二模理科数学试卷内蒙古北方重工业集团有限公司第三中学2020届高三下学期第四次模拟考试数学(理)试题内蒙古包头市北重三中2020届高三高考数学(理科)四模试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)北京市第一七一中学2020—2021学年高二数学3月月考试题北京市第一七一中学2023-2024学年高二下学期3月月考数学试题广西南宁市2018-2019学年高二下学期“4+ N”高中联合体期末数学(理)试题福建省莆田锦江中学2020-2021学年高二上学期期末考试数学试题
11-12高三下·北京朝阳·阶段练习
名校
6 . 在如图所示的几何体中,四边形
为平行四边形,
,
平面
,
,
,
,且
是
的中点.
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的大小;
(Ⅲ)在线段
上是否存在一点
,使得
与
所成的角为
? 若存在,求出
的长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d7b8c8a8aaff1053b0677cdd3539d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45d1180cb19d139a950b27306035a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac4401d39079cc4284b1d5977b8c922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71337caec78cbfb07b7501e8ccc92a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4f8bd9f03a28dc5ab676159930a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dceb5c62469c42bc018e2da4e7fbb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4bb9571b33d88f735fe6dc8fe41209.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b40bf08cb4c6a1d815882c13bd4216.png)
(Ⅲ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21002725043bdace95b3244d4c75dd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a0eb6045369a13358f2d5999f7bc3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://img.xkw.com/dksih/QBM/2012/4/23/1570839413678080/1570839419084800/STEM/a9e4fe8df22e4261877676a8988cb63b.png?resizew=302)
您最近一年使用:0次
11-12高三上·广东云浮·阶段练习
名校
解题方法
7 . 在如图所示的多面体中,
平面
,
,
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2011/11/28/1570364551266304/1570364556648448/STEM/d626437d-48d7-4b0f-a14b-f6abef876423.png?resizew=200)
(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/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4a6b8ef3e79b4482388c3391d8b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29f27c9a3af7044faf147bdaeb3fe81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4ffb68a9ca3bf66788363bc89dab45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bd9e8b54864ca44115d24a5aeeb83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70801d43498c8ae772b960f0353131f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1496042c1d721cffd25053e997a9a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6922690417492dea5c60acd5f031efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2011/11/28/1570364551266304/1570364556648448/STEM/d626437d-48d7-4b0f-a14b-f6abef876423.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03fcadd3ed6d1b8102d6260091e0bbdb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96bc9a285172c48e4726ee6492670ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2016-12-01更新
|
890次组卷
|
5卷引用:北京市海淀八模2019届高三理科数学模拟测试卷(二)
北京市海淀八模2019届高三理科数学模拟测试卷(二)(已下线)2012届广东省云浮罗定中学高三11月月考理科数学试卷湖南省长郡中学2018届高三月考(五)理科数学试题【全国百强校】河北省衡水中学2018届高三下学期第9周周考理科数学试题【全国百强校】宁夏石嘴山市第三中学2019届高三下学期一模考试数学(理)试题
2011·北京石景山·一模
8 . 在棱长为2的正方体ABCD—A1B1C1D1中,E,F分别为A1D1和CC1的中点.
![](https://img.xkw.com/dksih/QBM/2011/4/6/1570104326553600/1570104331878400/STEM/7d1705ace184438aab88b961415e3259.png?resizew=199)
(Ⅰ)求证:EF//平面ACD1;
(Ⅱ)求异面直线EF与AB所成的角的余弦值;
(Ⅲ)在棱BB1上是否存在一点P,使得二面角P—AC—B的大小为30°?若存在,求出BP的长;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2011/4/6/1570104326553600/1570104331878400/STEM/7d1705ace184438aab88b961415e3259.png?resizew=199)
(Ⅰ)求证:EF//平面ACD1;
(Ⅱ)求异面直线EF与AB所成的角的余弦值;
(Ⅲ)在棱BB1上是否存在一点P,使得二面角P—AC—B的大小为30°?若存在,求出BP的长;若不存在,请说明理由.
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名校
9 . 如图,在四棱锥
中,
底面
,底面
为梯形,
,
,且
.
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572519011819520/1572519017799680/STEM/2c7ab1d8cb304433adc2113bef588fb3.png?resizew=284)
(Ⅰ)若点
为
上一点且
,证明:
平面
;
(Ⅱ)求二面角
的大小;
(Ⅲ)在线段
上是否存在一点
,使得
?若存在,求出
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.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/c401700815c6e7814cba8bccfb35cd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a86542e55ad35b90a5c7afd23e8803.png)
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572519011819520/1572519017799680/STEM/2c7ab1d8cb304433adc2113bef588fb3.png?resizew=284)
(Ⅰ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8a5fc1d31b0f1a85e09336494c2e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f70cf3f6c7acbf60d4a4ca0ce89619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2425afeae790f548529e24c81a40560c.png)
(Ⅲ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be9f0a4775f2f15b4c9d412b52ede88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
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2016-12-04更新
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935次组卷
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7卷引用:2016届北京市海淀区高三上学期期末考试理科数学试卷
2016届北京市海淀区高三上学期期末考试理科数学试卷北京市西城区第8中学2017届高三上学期12月月考数学试题北京市昌平临川育人学校2018届高三12月月考数学(理)试题【全国百强校】北京市西城区第八中学2017届高三上12月月考数学(理)试题北京市首都师范大学第二附属中学2021届高三下学期开学考试数学试题2017-2018年北京市首都师大附中高二期末理试题(已下线)7.6 空间向量求空间距离(精讲)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)
名校
10 . 在四棱锥
中,底面
为正方形,
底面
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/33497f33-adb9-4258-9fc4-5513127b2d08.png?resizew=186)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值;
(3)若
为
中点,棱
上是否存在一点
,使得
,若存在,求出
的值,若不存在,说明理由.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1f2275769a49d61b7d94304dc2d0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/33497f33-adb9-4258-9fc4-5513127b2d08.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(3)若
![](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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790d5327d89fc1b3145e546482a46a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4838797cff70efabc1e8c1c005e3d6.png)
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2016-12-04更新
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1515次组卷
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5卷引用:2016届北京市东城区高三上学期期末考试理科数学试卷