解题方法
1 . 如图,在直三棱柱
中,
,
,
为
的中点,
,垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/6e958206-e24e-495d-aabf-03fa4c124748.png?resizew=126)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f868db591e0e98d5ec027f3388aecca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11cc02057010840ac28d0becb448dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/6e958206-e24e-495d-aabf-03fa4c124748.png?resizew=126)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504a36c231b8e80724d01649e7c0944f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
您最近一年使用:0次
名校
2 . 已知底面
是正方形,
平面
,
,
,点
、
分别为线段
、
的中点.
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)线段
上是否存在点
,使得直线
与平面
所成角的正弦值是
,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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab738b69adbbb752d38411395ab8e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c552df4af28e6a0a7cb993731958fddf.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50839c95d7a2adf8f0faf6ee182d20e0.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4613db540c9cb6a9d7e963bf89c2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c133b31ab3c50dc87d80879bbb0633.png)
(3)线段
![](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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4613db540c9cb6a9d7e963bf89c2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924d32b574fe69e43724304cf39513e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4838797cff70efabc1e8c1c005e3d6.png)
您最近一年使用:0次
2023-03-31更新
|
2719次组卷
|
12卷引用:天津市南开区南开中学2024届高三上学期统练6数学试题
天津市南开区南开中学2024届高三上学期统练6数学试题天津市十二区重点学校2023届高三下学期毕业班联考(一)数学试题(已下线)专题07立体几何的向量方法天津市耀华中学2024届高三上学期第一次月考数学试题(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天津市咸水沽第一中学2023-2024学年高三上学期期中考试数学试题天津市武清区英华实验学校2023-2024学年高二上学期第三次统练数学试题河南省洛阳市偃师高级中学2022-2023学年高一下学期4月月考数学试题(已下线)黄金卷04(已下线)专题7.3 空间角与空间中的距离问题【九大题型】天津市西青区杨柳青第一中学2023-2024学年高二下学期第一次质量检测数学试题天津市蓟州区第一中学2024届高三第一次校模拟考数学试卷
解题方法
3 . 如图,直四棱柱
的底面为正方形,P,O分别是上、下底面的中心,E是AB的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/e25ce1e5-e32d-4d0b-9f0a-bf91490172a8.png?resizew=220)
(1)求证:
平面
;
(2)当
时,求直线
与平面
所成角的正弦值;
(3)当k取何值时,O在平面
内的射影恰好为
的重心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5254f01a199d19ac9a1371d87249336e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/e25ce1e5-e32d-4d0b-9f0a-bf91490172a8.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3506f78513da0b4a5c522246e71c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc66cd5ccd5a579a42c6a241c62d764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)当k取何值时,O在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在直三棱柱
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/882f8981-a3b4-461b-aabd-767ca33bd321.png?resizew=135)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099edd3520292558184521a9af4e9064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d261edf9b4cfa7232e2bc184db1995.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/882f8981-a3b4-461b-aabd-767ca33bd321.png?resizew=135)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993830e5de2bbf858071d375bbf186f8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2023-02-22更新
|
592次组卷
|
2卷引用:天津市南开区2022-2023学年高二上学期1月阶段性质量监测数学试题
名校
解题方法
5 . 如图,在多面体
中,底面
为正方形,
平面
,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/85173386-fd46-4e45-b0fb-07ed636f8b29.png?resizew=171)
(1)求证:
平面
;
(2)若
,求
与平面
所成角的正弦值;
(3)若
平面
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8015cb25a477e921afee820e747c2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/85173386-fd46-4e45-b0fb-07ed636f8b29.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc521258fcaeaf7acffc5ae98c3af6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4280be91682e5d8a0d0704190319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
2023-01-06更新
|
648次组卷
|
3卷引用:天津市第九中学2022-2023学年高三上学期期末数学试题
天津市第九中学2022-2023学年高三上学期期末数学试题河北省邯郸市魏县2022-2023学年高二上学期期末考试数学试题(已下线)河北省石家庄市河北省实验中学2024届高三上学期名校联考数学试题变式题19-22
名校
解题方法
6 . 如图,在正方体
中,点M,N分别是
,
的中点,则下述结论中正确的个数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/1c6dc885-a3e9-4a1b-8d7e-2fd43efd0d6b.png?resizew=148)
①
∥平面
; ②平面
平面
;
③直线
与
所成的角为
; ④直线
与平面
所成的角为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/1c6dc885-a3e9-4a1b-8d7e-2fd43efd0d6b.png?resizew=148)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c170e8d26223ae423597d0d5a44a14d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9210bbf97012e7da54167521d0d0a6.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580a118fb0cbf4f3e690bf08a73700ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-12-08更新
|
1331次组卷
|
11卷引用:天津市天津中学2022-2023学年高二上学期期末数学试题
天津市天津中学2022-2023学年高二上学期期末数学试题河南省开封市2023届高三第一次模拟考试理科数学试题河南省开封市2023届高三年级第一次模拟考试文科数学试题 (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)-3(已下线)模块五 空间向量与立体几何-1江西省宜春市丰城市2022-2023学年高二上学期1月期末考试数学试题(已下线)6.3.3空间角的计算(2)河南省信阳高级中学2023届高三下学期开学考试文科数学试题(已下线)1.4.2用空间向量研究距离、夹角问题(第2课时)(已下线)艺体生一轮复习 第七章 立体几何 第36讲 空间向量在立体几何中的应用【练】(已下线)专题01 空间向量与立体几何(2)
解题方法
7 . 已知在直三棱柱
中,
,且
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/8e0529dd-d2da-4ad8-a33f-083804d2a16f.png?resizew=183)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667661dd4aba3a7564b286fda89f4491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/8e0529dd-d2da-4ad8-a33f-083804d2a16f.png?resizew=183)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43cbc92b5f5c26c7f70b52b27616a81.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43819ab7b268a6293a9251935b594690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14373a1c5a966e9f0af94d7786784a5.png)
您最近一年使用:0次
8 . 如图,在多面体中,底面
为菱形,
平面
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/90bf7a8d-ea1c-4c1d-b738-5e68126d0519.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f70cf3f6c7acbf60d4a4ca0ce89619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
您最近一年使用:0次
2022-11-10更新
|
825次组卷
|
3卷引用:天津市南开区2022-2023学年高三上学期11月阶段性质量监测(一)数学试题
名校
解题方法
9 . 为方便师生行动,我校正实施翔宇楼电梯加装工程.我们借此构造了以下模型:已知正四棱柱
,它抽象自翔宇楼南侧楼心花园所占据的空间,设
,
,O为底面ABCD的中心,正四棱柱
与正四棱柱
分别代表电梯井与电梯厢,设
,M为棱
的中点,N,K分别为棱
,
上的点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/0b462e61-384a-4f3f-84fa-ed7f0a03c599.png?resizew=243)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)“你站在桥上看风景,看风景的人在楼上看你.明月装饰了你的窗子,你装饰了别人的梦.”卞之琳诗句中的情景其实正在我们的生活中反复上演,上官琐艾同学站在楼心花园的中心(O点),她正目送着倚立在电梯厢一角的欧阳南德同学,假定上官同学的目光聚焦于棱OO2的中点I,此时,电梯厢中欧阳同学的目光正徘徊在位于N点的数学办公室与位于K点的数学实验室,当电梯厢向上启动时,在这时空里便诞生了由点O与移动着的平面INK所勾勒的动人风景.现在,请作为“正在看风景的人”的你完成以下问题:当电梯厢自底部(平面OECF与平面ABCD重合)运行至顶端(平面
与平面
重合)的过程中,点O到平面INK距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1300c053fde2be0861a4d128645dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaba7d7d6f2f3d6d4a2fe85d3c427f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38158de5a7c1ae8bc7a8ec9e1b90cf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca71c2f5005f86b706a3fc8bae97017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1dd2d3ebf5f4e9128f5a2f18018866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fb289ca6025309e93e3c20ac0f04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e023f80e4146cf44fd01935d0680f3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5594a4b5f0e842213df907dbb25c25cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/0b462e61-384a-4f3f-84fa-ed7f0a03c599.png?resizew=243)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f3477c7e6f5e94eac65dda58544d41.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc526324e78e4d9226d1b537f27845a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f3477c7e6f5e94eac65dda58544d41.png)
(3)“你站在桥上看风景,看风景的人在楼上看你.明月装饰了你的窗子,你装饰了别人的梦.”卞之琳诗句中的情景其实正在我们的生活中反复上演,上官琐艾同学站在楼心花园的中心(O点),她正目送着倚立在电梯厢一角的欧阳南德同学,假定上官同学的目光聚焦于棱OO2的中点I,此时,电梯厢中欧阳同学的目光正徘徊在位于N点的数学办公室与位于K点的数学实验室,当电梯厢向上启动时,在这时空里便诞生了由点O与移动着的平面INK所勾勒的动人风景.现在,请作为“正在看风景的人”的你完成以下问题:当电梯厢自底部(平面OECF与平面ABCD重合)运行至顶端(平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9f13896a66e307f01afe9ff43a82f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
您最近一年使用:0次
2022-11-06更新
|
356次组卷
|
4卷引用:天津市南开中学2022-2023学年高二上学期阶段性质量检测(一)数学试题
天津市南开中学2022-2023学年高二上学期阶段性质量检测(一)数学试题1.4空间向量的应用(已下线)期中真题必刷压轴60题(18个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)第六章 突破立体几何创新问题 专题二 融合科技、社会热点 微点3 融合科技、社会热点等现代文化的立体几何和问题综合训练【培优版】
名校
解题方法
10 . 如图,
平面
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7f68c056-f362-451b-ac15-7f03d54bd305.png?resizew=228)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)若二面角
的余弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80637f43cf748a2ce0aaf4cd0037749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883200c4d4e82a5411064a644aabfe33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bb994c172c6e9a318f6bef13d149c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fa988a1b4a8e1ef706f8ff773b038d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc82184408c19cc5f3474be38def4dc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7f68c056-f362-451b-ac15-7f03d54bd305.png?resizew=228)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d888c0b616792a2c41ff180de99fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4e1bdc9d0df390a30d7c27d6d3a0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1dd362f843e640ce551ad1787c9873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2022-10-20更新
|
574次组卷
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6卷引用:天津市南开中学2023-2024学年高三上学期第五次统练数学试题
天津市南开中学2023-2024学年高三上学期第五次统练数学试题新疆乌鲁木齐市第八中学2023届高三上学期第一次月考数学(理)试题山东省青岛市部分中学2022-2023学年高二上学期12月教学质量检测数学试题广东省人大附中深圳学校2022-2023学年高二上学期期末数学试题山东省青岛市青岛第二中学2022-2023学年高二上学期12月月考数学试题(已下线)第一章 空间向量与立体几何(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)