名校
解题方法
1 . 如图,
,
分别是直径
的半圆
上的点,且满足
,
为等边三角形,且与半圆
所成二面角的大小为
,
为
的中点.
平面
;
(2)在弧
上是否存在一点
,使得直线
与平面
所成角的正弦值为
?若存在,求出点
到平面
的距离;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e925392d0bf25a1a5c698ec1d8adea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)在弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab8a10e675354fa0c6e7da3d06b999d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93919b1b42b96052bb1ef51d2c6e90c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab8a10e675354fa0c6e7da3d06b999d.png)
您最近一年使用:0次
2024-03-20更新
|
671次组卷
|
4卷引用:黑龙江省大庆铁人中学2023-2024学年高二下学期开学考试数学试题
名校
2 . 如图,在四边形
中(如图1),
,
=
分别是边
上的点,将
沿
翻折,将
沿
翻折,使得点
与点
重合(记为点
),且平面
平面
(如图2)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/1ccde777-bef6-4ca6-8be5-8b1749599f33.png?resizew=293)
(1)求证:
;
(2)求二面角
余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60663fe74a7d36de97b28a37a68e5812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d2431ed9c0e3c333b77882b76f9cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532b3981b59bbc3bd1a3fe16f92a3027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0436efefa53aad714565ab2ba7ff90fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81641a4693e44c4194875790bcccb58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e154cbea71fa13440a81dbfa002c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012bd742142c39a1c1de8830e778bb70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/1ccde777-bef6-4ca6-8be5-8b1749599f33.png?resizew=293)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288142497e082cae14f8f145243da9f3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afb434b4ab457497962d27dd015d094.png)
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名校
解题方法
3 . 如图所示,棱长为3的正方体
中,
为线段
上的动点(不含端点),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.当![]() ![]() ![]() |
您最近一年使用:0次
2024-03-10更新
|
299次组卷
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2卷引用:黑龙江省大庆外国语学校2023-2024学年高二下学期开学质量检测数学试卷
名校
解题方法
4 . 如图,棱长为2的正方体
中,
,
分别为
,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/db7c7654-e150-4540-a927-6007e8cd002d.png?resizew=160)
A.![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2024-02-12更新
|
397次组卷
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2卷引用:黑龙江省大庆市大庆中学2024届高三下学期开学考试数学试题
解题方法
5 . 在空间直角坐标系中,已知点
,则点
到直线
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22214ceabd0508f3553c4f1f529c8a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2024-01-27更新
|
173次组卷
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2卷引用:黑龙江省哈尔滨师范大学青冈实验中学校2023-2024学年高二下学期开学考试数学试题
名校
6 . 如图,在直三棱柱
中,
,侧面
是正方形,且平面
平面
.
(1)求证:
;
(2)当AC与平面
所成的角为
,在线段
上是否存在点E,使平面ABE与平面BCE的夹角为
?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/a38f4e32-9f6a-4c28-938e-71888e26cd44.png?resizew=123)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)当AC与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
您最近一年使用:0次
2023-12-19更新
|
604次组卷
|
3卷引用:黑龙江省大兴安岭实验中学(东校区)2023-2024学年高二下学期期初考试数学试题
黑龙江省大兴安岭实验中学(东校区)2023-2024学年高二下学期期初考试数学试题山东省名校考试联盟2024届高三上学期12月阶段性检测数学试题(已下线)专题13 空间向量的应用10种常见考法归类(3)
名校
7 . 如图,在四棱锥
中,
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/e3aafac1-6f9c-4327-87ef-794afc4414d5.png?resizew=176)
(1)求证:
面
;
(2)点
在棱
上,设
,若二面角
余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044023bf62e87cb9002ba2974f74bc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc10330e0827026b78343a4f0ead282f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29c9bf1a6582c093b30e429f3b6ca9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/e3aafac1-6f9c-4327-87ef-794afc4414d5.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34cf4760da098099493d4627dacb878.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a7d6e106dbdb0ae79f77462faf768a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deffc349cbe3464f41c7965d32ef53b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-10-27更新
|
2038次组卷
|
7卷引用:黑龙江省大庆外国语学校2023-2024学年高二下学期开学质量检测数学试卷
名校
8 . 如图,在三棱柱
中,
分别为
的中点,且
平面
.
(1)求证:
面
;
(2)求棱
的长度;
(3)若
,且
的面积
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657445b7b8df96d3b173012fde931d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6624bd01cd267b6ff12d926460048b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/78f81c82-dd61-496c-8475-50008fbe10a7.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b45b3bcea638fc84e8fe6d6b1b5317e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e56c43b15982d6db10a221fcba6ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27bff7b3b85a8fb2a8d360ce15065aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1bfd3f793901e03f3259020643423d.png)
您最近一年使用:0次
名校
解题方法
9 . 四棱锥
的底面是正方形,
平面ABCD,E,F分别是AB,PD的中点,且
.
(1)求证:
平面PEC;
(2)求直线BF与平面PEC所成角的正弦值.
![](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/c3b10835116b9b777a666b438c907b49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/2/7ffbc579-5776-4aac-970a-3eeb6a5224a1.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
(2)求直线BF与平面PEC所成角的正弦值.
您最近一年使用:0次
2023-09-01更新
|
340次组卷
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2卷引用:黑龙江省哈尔滨市第三中学校2023-2024学年高二上学期开学测试数学试题
名校
解题方法
10 . 如图,四边形
与四边形
是全等的矩形,
.
(1)若P是棱
的中点,求证:平面
平面
;
(2)若P是棱
上的点,直线BP与平面
所成角的正切值为
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cacb5e127e36bc0d2fe22398849c46.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/28/39c1bc63-55bc-4ede-a75d-79a427f0ff40.png?resizew=232)
(1)若P是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6f775b7677f38503d77a7daf2dce85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275cb08430f635054519c543b72303f.png)
(2)若P是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dedfba8b9447a4db53baae62fdeebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b330018216e02c49a6621b6c964ccd3c.png)
您最近一年使用:0次
2023-08-26更新
|
438次组卷
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3卷引用:黑龙江省双鸭山市第一中学2023-2024学年高二上学期开学考试数学试题
黑龙江省双鸭山市第一中学2023-2024学年高二上学期开学考试数学试题安徽省池州市贵池区2023-2024学年高二上学期期中教学质量检测数学试卷(已下线)第03讲 第一章空间向量与立体几何章节综合测试(原卷版)