名校
1 . 如图,在四棱锥
中,
,
平面PAB,
且
,F为PC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/8ea29f08-dd31-4c91-b1d1-0bd2965d166f.png?resizew=241)
(1)求证:
平面PAB;
(2)求直线PD与平面PBC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860c4c9419ebfa927b3f3ea14e4f4784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0787d2cb66d00c49d3348b52acd407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2992befbac3f901fdbbdc75b7f6a8de5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/8ea29f08-dd31-4c91-b1d1-0bd2965d166f.png?resizew=241)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
(2)求直线PD与平面PBC所成角的正弦值.
您最近一年使用:0次
2022-06-28更新
|
531次组卷
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6卷引用:浙江省温州市新力量联盟2021-2022学年高二下学期期末联考数学试题
名校
2 . 如图,在四棱锥
中,底面
为矩形,侧面
是等腰三角形且
为
的中点,
在
上且
底面
.
侧面
;
(2)当底面
为正方形且侧面
为等边三角形时,求二面角
的平面角
的正切值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef25f6a76dd6b1529a1ab57d5ab0b66f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)当底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053af8641980763a7f0e77beefe0712d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2022-06-27更新
|
1301次组卷
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6卷引用:浙江省宁波市慈溪市2021-2022学年高一下学期期末数学试题
解题方法
3 . 如图, 四棱锥
的底面四边形
为正方形, 顶点
在底面的射影为线段
的中点
是
的中点, ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899cd04d0ea417f9e1e0ff317dfe171e.png)
(1)求证:
平面
;
(2)求过点
的平面截该棱锥得到两部分的体积之比.
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70e70bd32076945ff38766105181431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899cd04d0ea417f9e1e0ff317dfe171e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/50e59e22-02a7-4a39-b364-5e155c8ca50a.png?resizew=264)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5979c684468fc369ad9b431b69bdd9c2.png)
您最近一年使用:0次
4 . 如图1,在
中,
,
,
,且
分别为BC,AD的中点,延长CE交AB于点F.现将△ACD沿AD翻折至△AC'D,使得
,如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/8b25cad7-4f05-4702-a9c6-93257f85a5df.png?resizew=493)
(1)求证:
;
(2)点G为线段C'D的中点,求直线FG与平面BEC'所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178a27068cf5517ad64f211af10256ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c7f0d0987ee427b7efbbf889b9bf16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794cd813dabab72619eb276f93c1769e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/8b25cad7-4f05-4702-a9c6-93257f85a5df.png?resizew=493)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed96a8bd80187c8ed5fdf272832ca8a4.png)
(2)点G为线段C'D的中点,求直线FG与平面BEC'所成角的正弦值.
您最近一年使用:0次
5 . 如图,已知
和
都是直角梯形,
,
,
,
,
,
,二面角
的平面角为
.设M,N分别为
的中点.
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26dbbd583ee4edd5a0fd537ce9e861d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40560ea08d6cd8c1d4d9661ee6faaa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502807a17f318c77921e75039fead278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bfc65bfbc357d43069e9aad18f8625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f892d82e656fd14e4464c0f04730d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdadcc147a7e441decf7561c9e7310e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-06-10更新
|
21079次组卷
|
33卷引用:2022年新高考浙江数学高考真题
2022年新高考浙江数学高考真题(已下线)2022年高考浙江数学高考真题变式题10-12题重庆市第八中学校2021-2022学年高二下学期期末复习数学试题(已下线)第06讲 向量法求空间角(含探索性问题) (讲)-3重庆市万州第二高级中学2022-2023学年高二上学期开学考试数学试题(已下线)2022年高考浙江数学高考真题变式题19-22题(已下线)第04讲 空间向量在立体几何中的应用(练,理科专用)湖北省武汉市第一中学2022-2023学年高三上学期10月月考数学试题湖南省永州市江华瑶族自治县第一中学2022-2023学年高三上学期12月月考数学试题(已下线)第07讲 空间向量的应用 (2)浙江省宁波市鄞州中学2023-2024学年高二上学期期中考试数学试题专题07立体几何与空间向量(已下线)专题40:空间角的向量求法-2023届高考数学一轮复习精讲精练(新高考专用)(已下线)模拟卷05(已下线)专题08 立体几何解答题常考全归类(精讲精练)-1江苏省扬州市仪征中学、江都中学2022-2023学年高三上学期期末阶段联考数学试题青海省西宁市海湖中学2022-2023学年高二下学期开学摸底考试数学试卷 A卷湖南省衡阳市衡阳县第四中学2022-2023学年高二平行班下学期开学模拟考试数学试题河南省洛阳市第八高级中学2023届高三下学期开学摸底考试理科数学试题江苏省南京市田家炳高级中学2022-2023学年高二下学期期初考试数学试题湖南省湘潭市湘潭县第一中学2022-2023学年高二下学期3月月考数学试题(已下线)专题八 立体几何-2(已下线)重组卷02(已下线)第4讲 空间向量的应用 (2)(已下线)专题19 空间几何解答题(理科)-3第一章 空间向量与立体几何 (单元测)(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)河南省许昌市禹州市高级中学2023-2024学年高三上学期11月月考数学试题(已下线)第05讲 空间向量及其应用(练习)(已下线)考点12 空间角 2024届高考数学考点总动员 【讲】(已下线)通关练05 空间向量与立体几何近五年高考真题4考点精练(30题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)模块一 专题6《 空间向量应用》 B提升卷 (苏教版)(已下线)专题23 立体几何解答题(理科)-1
解题方法
6 . 如图,在三棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
的体积和表面积
(2)若E、F分别为PA、PB的中点,求证
面EFC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9b8e7befcb7881c294070175b1a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5064f5ce5ac8428e277fd578da84ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d715e6b470395136a6c4215dbe6ff82e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)若E、F分别为PA、PB的中点,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2cfa68b1900da8c1a71dd832872689.png)
您最近一年使用:0次
2022-04-13更新
|
283次组卷
|
2卷引用:浙江省台州市玉环市玉城中学2021-2022学年高一下学期第一次月考数学试题
名校
7 . 如图,在三棱锥
中,
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/6c27cf44-4bf4-4a15-acea-dfe23eedfdf1.png?resizew=161)
(1)证明:平面
平面
;
(2)若
,直线
与平面
所成角的大小为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42deb6707a04e7810c10a8370f2422d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/6c27cf44-4bf4-4a15-acea-dfe23eedfdf1.png?resizew=161)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6e6192cf24ada791c26c2d6d434069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
您最近一年使用:0次
2022-06-23更新
|
1110次组卷
|
2卷引用:浙江省宁波市2021-2022学年高二下学期期末数学试题
8 . 如图,在三棱柱
中,底面
是正三角形,侧面
为菱形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/f0521453-0004-4a1a-808b-497a88306cd5.png?resizew=243)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be445f94888b34161b6d59d458928e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aa3abd2a06b944b8ddea23337eae6e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/f0521453-0004-4a1a-808b-497a88306cd5.png?resizew=243)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
名校
9 . 如图,已知三棱台
中,点
在平面
内的射影D在
上,
,
,
,M,N分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987806771306496/2989879580712960/STEM/8d683646-d93f-428a-80d0-e46dcb7495b3.png?resizew=264)
(1)证明:直线
平面
;
(2)若
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97315b1fc75dc5bb8569d6fcb2cd668f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad7abb9d770021c6e498ca49d45f974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987806771306496/2989879580712960/STEM/8d683646-d93f-428a-80d0-e46dcb7495b3.png?resizew=264)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988ac0247c60cbb622f2330276c6190d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
名校
10 . 如图,在直四棱柱
中,底面
是边长为1,且
的菱形,侧棱长为2,
是侧棱
上的一点,
.
,使直线
与平面
所成的角为
;
(2)在线段
上是否存在一个定点
,使得对任意的
,有
,并证明你的结论.
![](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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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