1 . 如图,四棱锥P-ABCD中, PA⊥平面ABCD,E为BD的中点,G为PD的中点,△DAB≌△DCB,EA=EB=AB=1,
,连接CE并延长交AD于F.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab58dfbc740745c55839f2f43c1886b.png)
(Ⅰ)求证:AD⊥CG;
(Ⅱ)求平面BCP与平面DCP的夹角的余弦值.
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,点
在棱
上,且
.
(Ⅰ)求证:
;
(Ⅱ)是否存在实数
,使得二面角
的余弦值为
?若存在,求出实数
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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facf189b2a3153beb7b9e077d3b1146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7ae4091a3a2767fde8e9f5a604c1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18fc2798b3ae9cc19eeb5ff488703e9.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/6822db67464507ee6997b93103003a36.png)
![](https://img.xkw.com/dksih/QBM/2018/2/25/1889951998967808/1895651440132096/STEM/2e8de1c52d1a48579609eb077b768f69.png?resizew=239)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
(Ⅱ)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeab80976db9b4689b9446cda06196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2018-03-05更新
|
1271次组卷
|
5卷引用:湖北省宜昌市2018届高三年级元月调研考试数学理试题
湖北省宜昌市2018届高三年级元月调研考试数学理试题(已下线)2018年高考数学备考中等生百日捷进提升系列(综合提升篇) 专题04 立体几何解答题(理)甘肃省天水市第一中学2019届高三一轮复习第六次质量检测数学(理)试题江西省新余市2019-2020学年高三上学期期末数学(理科)试题广东省汕头市澄海中学2020届高三下学期开学前测试数学试题
名校
3 . (衡水金卷2018年普通高等学校招生全国统一考试模拟试卷)如图,在三棱柱
中,侧棱
底面
,且
,
是棱
的中点,点
在侧棱
上运动.
(1)当
是棱
的中点时,求证:
平面
;
(2)当直线
与平面
所成的角的正切值为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83460397189a6b0d1032c5c6cc585914.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/9d88bf46ad08f9677c37eed1d0369329.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaf8d068559d90824eb43b9c252a320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f8ebfd36ca360f2c516541a31254ad.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a848020a0d6420af76ec7bbadc9cdf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c6dbe3dde6e5b84a240b2baf87201.png)
![](https://img.xkw.com/dksih/QBM/2018/6/15/1967883896307712/1968997421285376/STEM/9907d2bf4fa1497f9e9d0db426a3e7de.png?resizew=110)
您最近一年使用:0次
2018-02-27更新
|
617次组卷
|
6卷引用:湖北省襄阳市2018-2019学年高二下学期期末数学(理)试题
湖北省襄阳市2018-2019学年高二下学期期末数学(理)试题衡水金卷2018年普通高等学校招生全国统一考试模拟试卷 分科综合卷 理科数学(一)(已下线)《高频考点解密》—解密16 空间向量与立体几何安徽省滁州市定远县育才学校2020-2021学年高二上学期第二次月考数学(理)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+分层训练海南省琼海市嘉积中学2022-2023学年高二上学期第二次月考数学试题
4 . 如图所示的几何体是圆柱的一部分,它是由矩形
(及其内部)以
边所在直线为旋转轴旋转
得到的,点
是弧
上的一点,点
是弧
的中点.
![](https://img.xkw.com/dksih/QBM/2018/2/11/1880014061846528/1887807304548352/STEM/95c40ac102384357858130db7de0d4a0.png?resizew=208)
(1)求证:平面
平面
;
(2)当
且
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39289d3709ba1e565b165c30ed981d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/2018/2/11/1880014061846528/1887807304548352/STEM/95c40ac102384357858130db7de0d4a0.png?resizew=208)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf42acb8d1875acf1775e30ae2e3d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d666dd3308604685e59f4ca22663b9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67df92b247a24871dfb0e7aaeb54a72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fb6724bf84166de9ffe36364849e60.png)
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名校
解题方法
5 . 已知长方体
,
,
,
为线段
上一点,且
,则
与平面
所成的角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/2018/2/11/1880146226372608/1883622971072512/STEM/02e41507639b4e01bc8451efcaad59b7.png?resizew=269)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.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/275d68d50a992cb17d948d3299012a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb4e4c148b9185e09e454955eaa7312.png)
![](https://img.xkw.com/dksih/QBM/2018/2/11/1880146226372608/1883622971072512/STEM/02e41507639b4e01bc8451efcaad59b7.png?resizew=269)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2018-02-16更新
|
568次组卷
|
16卷引用:湖北省黄石市2019-2020学年高二上学期期末数学试题
湖北省黄石市2019-2020学年高二上学期期末数学试题山东省菏泽市2017-2018学年高二上学期期末考试数学(理)试题河南省林州市第一中学2017-2018学年高二(普通班)上学期期末考试数学(理)试题(已下线)2018年高考数学备考中等生百日捷进提升系列(捷进提升篇)专题08 立体几何(已下线)第三章++空间向量与立体几何(能力提升)-2020-2021学年高二数学单元测试定心卷(人教版选修2-1)(已下线)专题8.6 立体几何中的向量方法-2021年高考数学(理)一轮复习-题型全归纳与高效训练突破(已下线)专题8.7 利用空间向量求空间角 (精练)--2021年高考数学(理)一轮复习讲练测(已下线)专题8.7 利用空间向量求空间角(精练)-2021年高考数学(理)一轮复习学与练(已下线)专题5.3 运用空间向量解决立体几何中的角与距离-备战2021年高考数学精选考点专项突破题集(新高考地区)(已下线)黄金卷19-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(江苏专用)重庆市两江育才中学2021-2022学年高二上学期第一次阶段性测试数学试题甘肃省民勤县第一中学2020-2021学年 第二学期 高二数学(理) 开学考试试卷吉林省洮南市第一中学2021-2022学年高二上学期第三次月考数学试卷题安徽省合肥市肥东县综合高中2022-2023学年高三上学期12月月考数学试题河南省济源市英才学校2022-2023学年高二上学期期末数学试题(已下线)期末精确押题之单选题(45题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
6 . 如图,在三棱锥
中,
两两垂直且相等,过
的中点
作平面
∥
,且
分别交PB,PC于M、N,交
的延长线于
.
![](https://img.xkw.com/dksih/QBM/2018/2/2/1873761807777792/1874529704992768/STEM/609759323a2941b6bfe31858e8915f59.png?resizew=168)
(Ⅰ)求证:
平面
;
(Ⅱ)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7654428b93930da90a37fc74a826c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://img.xkw.com/dksih/QBM/2018/2/2/1873761807777792/1874529704992768/STEM/609759323a2941b6bfe31858e8915f59.png?resizew=168)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc72e22c2c9701c1ec79c4a1c10951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d905520a2c15614e156f778f24a0d2f3.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在四棱锥
中,已知
且四边形ABCD为直角梯形,
分别为PA,PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/b474c605-77b8-48c7-975e-47eba0039187.png?resizew=195)
(1)求证:
平面
;
(2)点Q是线段BP上的动点,当直线CQ与DM所成角最小时,求线段BQ的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8841a3500a2c2c11437f9ee4eb24fc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dead78913a272a84ecc44bbbeb8f08.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/b474c605-77b8-48c7-975e-47eba0039187.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)点Q是线段BP上的动点,当直线CQ与DM所成角最小时,求线段BQ的长.
您最近一年使用:0次
2018-02-02更新
|
672次组卷
|
3卷引用:【校级联考】湖北省龙泉中学、随州一中、天门中学三校2019届高三四月联考理科数学试题
名校
8 . 已知四边形
为等腰梯形,
,
沿对角线将
旋转,使得点
至点
的位置,此时满足
.
(1)判断
的形状,并证明;
(2)求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea583e7b2d2a4e51679d2e06724b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65334978b0519b379910dfc4acf8344.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9017cfed5393f9b21602107ed164c733.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/e4e77187-27e1-4e3f-ba88-49e0fc6d5a95.png?resizew=370)
您最近一年使用:0次
2018-01-25更新
|
456次组卷
|
3卷引用:湖北省黄石市阳新县兴国高级中学等三校2022-2023学年高二上学期期末线上测试数学试题
名校
解题方法
9 . 如图,在直三棱柱
中,
、
分别为
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2018/1/23/1866727688790016/1867196986048512/STEM/11ff22898b9c4dcf9b02d94df857da3d.png?resizew=171)
(1)求证:平面
平面
;
(2)若直线
和平面
所成角的正弦值等于
,求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3e8d881d96688ea15a868bb5a39f59.png)
![](https://img.xkw.com/dksih/QBM/2018/1/23/1866727688790016/1867196986048512/STEM/11ff22898b9c4dcf9b02d94df857da3d.png?resizew=171)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456175ea34492f0bc025aaab668fa659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
您最近一年使用:0次
2018-01-24更新
|
1028次组卷
|
5卷引用:湖北省仙桃中学2018-2019学年高三上学期期中数学(理)试题
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解题方法
10 . 如图,PD垂直正方形ABCD所在平面,AB=2,E是PB的中点,
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/4ec3942f-4e5d-42cf-8bf4-92c7a45fdf1c.png?resizew=153)
(1)建立适当的空间坐标系,求出点E的坐标;
(2)在平面PAD内求一点F,使EF⊥平面PCB.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef83383a6e1ef8e483a712347e678d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00b863991d441829e9ccbc21a796301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8a0eb3271be142d81217379f3947af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/4ec3942f-4e5d-42cf-8bf4-92c7a45fdf1c.png?resizew=153)
(1)建立适当的空间坐标系,求出点E的坐标;
(2)在平面PAD内求一点F,使EF⊥平面PCB.
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2018-01-12更新
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6卷引用:湖北省襄阳市老河口市第一中学2022-2023学年高二上学期期末数学试题
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