1 . 如图,在四棱锥
中,底面
中,底面
满足
,
,
底面
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/681520f2-0694-477d-bef7-a2525a026d8e.png?resizew=197)
(1)证明:
;
(2)求平面
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/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.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/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/681520f2-0694-477d-bef7-a2525a026d8e.png?resizew=197)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2020-12-15更新
|
143次组卷
|
2卷引用:湖北省荆门市沙洋中学2020-2021学年高二上学期12月月考数学试题
2 . 如图,在三棱锥
中,
,
,侧面
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/0f38aaa5-b0b0-4c4b-815b-564b9dc08370.png?resizew=139)
(1)求证:
是直角三角形;
(2)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/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/0f38aaa5-b0b0-4c4b-815b-564b9dc08370.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284b8b2b9efda0cad865cd9248a95112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
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2020-09-23更新
|
158次组卷
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2卷引用:湖北省荆门市钟祥市实验中学2020-2021学年高二下学期4月阶段检测(2)数学试题
名校
解题方法
3 . 在直三棱柱
中,
,
,
,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe236a434aa88e5633ea61574d1bed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-07-11更新
|
589次组卷
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3卷引用:湖北省荆门市2018-2019学年高一下学期期末数学试题
湖北省荆门市2018-2019学年高一下学期期末数学试题安徽省合肥一中2019-2020学年高二(上)期中数学(理科)试题(已下线)专题8.7 立体几何中的向量方法(精练)-2021年新高考数学一轮复习学与练
名校
解题方法
4 . 如图在四棱锥
中,平面
底面ABCD,底面ABCD是等腰梯形,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
.
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480342232137728/2480701720436736/STEM/9dde8ca597b34fdabdb928ae2b5dd6f1.png?resizew=168)
(1)证明:
.
(2)求平面PCD与平面PAB夹角(锐角)的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab40c3da31f132ceded9671f5020ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a0c299356c26338d4153748e8a61d.png)
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480342232137728/2480701720436736/STEM/9dde8ca597b34fdabdb928ae2b5dd6f1.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c231fb9aeaf4b73c2d835bb4c3d42b.png)
(2)求平面PCD与平面PAB夹角(锐角)的余弦值.
您最近一年使用:0次
2020-06-09更新
|
455次组卷
|
3卷引用:湖北省荆门市龙泉中学2020届高三下学期高考适应性考试(二)数学(理)试题
名校
解题方法
5 . 如图,直三棱柱
的底面为等边三角形,
、
分别为
、
的中点,点
在棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/5b818423-f024-4cb1-9f3e-0e3cb64ef6d1.png?resizew=172)
(1)证明:平面
平面
;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51352936f13995f63cd74207c303971a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/5b818423-f024-4cb1-9f3e-0e3cb64ef6d1.png?resizew=172)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890aa7b375e3a8f8f8a0f36cf5deca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41861a8201bf8378a05a09ae0bd84635.png)
您最近一年使用:0次
2020-05-21更新
|
599次组卷
|
3卷引用:湖北省荆门市龙泉中学2020-2021学年高三上学期11月月考数学试题
名校
解题方法
6 . 如图所示,已知四边形
是菱形,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/2cf5aecf-039e-4cd2-9ed1-e1074edad764.png?resizew=142)
(1)求证:平面
平面
.
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e09e045bbd617f55327c1585cd837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66784e61bb8be33243a208895fc2ae08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aa755bb93da4f4d53ee091f6a59742.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/2cf5aecf-039e-4cd2-9ed1-e1074edad764.png?resizew=142)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1507da3daed983c2f355d4caebb66d72.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e2132b711f5aa21a0048ad3fc37f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d822b2c1a7c36973654513338f04d821.png)
您最近一年使用:0次
2020-05-12更新
|
485次组卷
|
4卷引用:湖北省荆门市龙泉中学2020届高三下学期高考适应性考试(一)理科数学试题
名校
7 . 在平行四边形
中,
,
,
,
是EA的中点(如图1),将
沿CD折起到图2中
的位置,得到四棱锥是
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453971677822976/2454901004050432/STEM/d5058c8c-a54b-40f9-9c97-196fb71047c7.png)
(1)求证:
平面PDA;
(2)若PD与平面ABCD所成的角为
.且
为锐角三角形,求平面PAD和平面PBC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb5d56b5ef73dc6046f1a11e1e18919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2761cf826c9f9850fb93071971a17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a05d97047e3a5c8e125d334d478ee8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6414089941feb5d8a4a6a49566b9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453971677822976/2454901004050432/STEM/d5058c8c-a54b-40f9-9c97-196fb71047c7.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)若PD与平面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8fe4026f1a0745ab9aa9fe64f0e482.png)
您最近一年使用:0次
2020-05-03更新
|
290次组卷
|
5卷引用:2020届湖北省荆门市高三下学期4月模拟考试理科数学试题
2020届湖北省荆门市高三下学期4月模拟考试理科数学试题2020届湖北省荆州中学、宜昌一中、龙泉中学三校联盟高三下学期4月联考理科数学试题西藏自治区拉萨市拉萨中学2019-2020学年高二第六次月考数学理科试卷(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)重庆市万州第三中学2020-2021学年高二上学期期中数学试题
名校
解题方法
8 . 如图,在四棱锥PABCD中,PA⊥平面ABCD,∠ABC=∠BAD=90°,AD=AP=4,AB=BC=2,M为PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/a18400c8-47ad-4a8d-a9fd-cc8b2f9e51c3.png?resizew=153)
(1)求异面直线AP,BM所成角的余弦值;
(2)点N在线段AD上,且AN=λ,若直线MN与平面PBC所成角的正弦值为
,求λ的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/a18400c8-47ad-4a8d-a9fd-cc8b2f9e51c3.png?resizew=153)
(1)求异面直线AP,BM所成角的余弦值;
(2)点N在线段AD上,且AN=λ,若直线MN与平面PBC所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
您最近一年使用:0次
2020-02-25更新
|
1541次组卷
|
8卷引用:湖北省荆门市龙泉中学2019年高三年级11月月考理科数学试题
湖北省荆门市龙泉中学2019年高三年级11月月考理科数学试题2017届江苏徐州等四市高三11月模拟考试数学卷(已下线)《2018届优生-百日闯关系列》数学专题三 第一关 以立体几何中探索性问题为背景的解答题【省级联考】江苏省2019届高三年级4月质量检测数学试题含附加题专题21 空间向量与几何体-《巅峰冲刺2020年高考之二轮专项提升》[江苏]2019届江苏省南京师大附中高三下学期5月模拟数学试题(已下线)专题04 立体几何的探索性问题(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖四川省成都市树德中学2020-2021学年高二下学期4月月考数学(理)试题
名校
9 . 如图,在菱形ABCD中,∠ABC=60°,E,F分别是边AB,CD的中点,现将△ABC沿着对角线AC翻折,则直线EF与平面ACD所成角的正切值最大值为
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/27767ec1-9364-4f8e-8b9f-16aaeb178a87.png?resizew=114)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/27767ec1-9364-4f8e-8b9f-16aaeb178a87.png?resizew=114)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-12-16更新
|
976次组卷
|
7卷引用:湖北省荆门市龙泉中学2020届高三下学期高考适应性考试(一)理科数学试题
湖北省荆门市龙泉中学2020届高三下学期高考适应性考试(一)理科数学试题2019年11月北京市清华大学中学生标准学术能力诊断性测试测试数学(理)试题(二卷)河南省顶级名校2019-2020学年高三尖子生11月诊断性检测数学(理)试卷(已下线)思想03 数形结合思想 第三篇 思想方法篇(讲)-2021年高考二轮复习讲练测 (浙江专用)(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)专题4.4 立体几何中最值问题-玩转压轴题,进军满分之2021高考数学选择题填空题浙江省嘉兴市第五高级中学2020-2021学年高二下学期期中数学试题
10 . 如图,在四棱锥S-ABCD中,
平面
,底面ABCD为直角梯形,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8f7251f98b8d6354782afd37462896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/a9f0a270-64e5-40bc-bc50-3bf1a65c51c1.png?resizew=165)
(Ⅰ)求
与平面
所成角的正弦值.
(Ⅱ)若E为SB的中点,在平面
内存在点N,使得
平面
,求N到直线AD,SA的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8f7251f98b8d6354782afd37462896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/a9f0a270-64e5-40bc-bc50-3bf1a65c51c1.png?resizew=165)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
(Ⅱ)若E为SB的中点,在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa00966462971fe7856c033f8cb1b821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
您最近一年使用:0次