1 . 在直三棱柱
中,四边形
是边长为4的正方形.
,
,
是
的中点.
(1)在
上求作一点
,使得
平面
,并证明;
(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/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
您最近一年使用:0次
2020-03-26更新
|
124次组卷
|
2卷引用:河北省沧州市第一中学2021-2022学年高二上学期第三次学段检测数学试题
2019·河北·模拟预测
2 . 如图,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c79f4d0ad59ae56e1c3a2712ad208ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/704ce96e-3d3a-476b-93fb-0b026adfff86.png?resizew=161)
(1)求证:
;
(2)求PB与面ABC所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c79f4d0ad59ae56e1c3a2712ad208ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/704ce96e-3d3a-476b-93fb-0b026adfff86.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b744fb89dfe126f9f78543ac53db006e.png)
(2)求PB与面ABC所成角的正切值.
您最近一年使用:0次
3 . 在
中,
,
,
平面ABC,
,D为VA中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/13b6439e-f2e8-417f-8896-0098bbcd6fe6.png?resizew=161)
(1)求证:
平面DBC;
(2)求DB与平面ABC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d01592b7e10bf087d1465f9d6899bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1385c59d0fe2bc62fed70a2d13a5e956.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/13b6439e-f2e8-417f-8896-0098bbcd6fe6.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c439e4e4e48b17e19e666d892216fe.png)
(2)求DB与平面ABC所成角的正弦值.
您最近一年使用:0次
4 . 如图,已知
,
.
![](https://img.xkw.com/dksih/QBM/2019/3/21/2165353812238336/2165990455443456/STEM/478fb0385fb54f2ca3d9cb8cfbd732c8.png?resizew=275)
(1)求证:面
面ABCD;
(2)若二面角
为60°,
,
,求PB与面ABCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecfe796b08bdf608bbee65af1388598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://img.xkw.com/dksih/QBM/2019/3/21/2165353812238336/2165990455443456/STEM/478fb0385fb54f2ca3d9cb8cfbd732c8.png?resizew=275)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1de92fc2b7a7c63f4c1b0de2b1e0157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fc6a5e71fa379d613ac1ef1cdf1048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a02e98a505b38aea5b8ee515520b41d.png)
您最近一年使用:0次
5 . 如图,
平面
,
,
,
,
分别为
的中点.(I)证明:
平面
;(II)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299aec7bf0fff4e5b8b0c59bf18ea726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aee33e4af8ef3bf5025d7e630abcfc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e975e7562572d24e6462e774f5fd491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b929f1f7b0c8cb489d29d0a6da6bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9c457e757ac146cbb07008c58944fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://img.xkw.com/dksih/QBM/2010/3/17/1569642148438016/1569642225819648/STEM/58889a40b9254d45a4e63686d46109c5.png)
您最近一年使用:0次
2019-01-30更新
|
2740次组卷
|
16卷引用:2010年河北省唐山一中高二第二学期期末考试数学(文)试卷
(已下线)2010年河北省唐山一中高二第二学期期末考试数学(文)试卷河北省武邑中学2017届高三下学期第三次模拟考试数学(文)试题河北省沧州市第三中学2019-2020学年高一下学期期末数学试题(已下线)2009年普通高等学校招生全国统一考试文科数学(浙江卷)(已下线)2010-2011年河南省许昌高一下学期第四次五校联考数学试卷(已下线)2010-2011年重庆市杨家坪中学高二下学期第一次月考数学理卷(已下线)2012-2013学年黑龙江哈尔滨第十二中学高二上期末考试理科数学卷2015届甘肃省天水市秦安县第二中学高三第五次检测文科数学试卷12015届甘肃省天水市秦安县第二中学高三第五次检测文科数学试卷22015-2016学年湖南长郡中学高一下第一次检测数学试卷2016-2017学年湖南省醴陵二中、醴陵四中高二下学期期中联考数学(文)试卷【全国百强校】宁夏银川一中2018-2019学年高一上学期期末考试数学试题(已下线)【新东方】高中数学20210527-010【2021】【高二下】云南省丽江市2020-2021学年高一下学期期末数学试题(已下线)考点20 直线、平面平行的判定及其性质-备战2022年高考数学(文)一轮复习考点微专题河南省顶级名校2021-2022学年高一下学期5月月考数学试题
6 . 如图,正方体
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(1)求证:平面
;
(2)求直线与平面
所成角的正弦值.
您最近一年使用:0次
2018-12-15更新
|
522次组卷
|
2卷引用:河北省唐山市开滦第二中学2019-2020学年高二上学期期中数学试题
7 . 如图所示,在正方体
中,
是
上一点,
是
的中点,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(Ⅰ)求证:
平面
;
(Ⅱ)求
与平面
所成的角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e89acc2b46a2ff0e61c894c56382b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2018/8/1/2001266564153344/2002457559318528/STEM/4e52e6bd0e504d5bbb28d9ea1185fc78.png?resizew=149)
您最近一年使用:0次
8 . 如图,四棱锥
中,
,
,
为
中点.
(1)证明:
平面
;
(2)若
平面
,
是边长为
的正三角形,求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d8af1e40a1febb02025c503a1fcf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8c7c8c8702adfbd6bcacc94a6bc661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/2018/6/4/1959949486522368/1961532367355904/STEM/0f7c1d8bf3bb41eaa3a43217f13dbd01.png?resizew=129)
您最近一年使用:0次
9 . 如图,四面体ABCD中,O,E分别是BD,BC的中点,CA=CB=CD=BD=2,AB=AD=
.
![](https://img.xkw.com/dksih/QBM/2018/2/28/1892119677173760/1895770480508928/STEM/123ca84b53944765871ba4e56cf9ebc8.png?resizew=132)
(1)求证:OE//平面ACD;
(2)求直线AC与平面BCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2018/2/28/1892119677173760/1895770480508928/STEM/123ca84b53944765871ba4e56cf9ebc8.png?resizew=132)
(1)求证:OE//平面ACD;
(2)求直线AC与平面BCD所成角的正弦值.
您最近一年使用:0次
2018-01-28更新
|
566次组卷
|
4卷引用:河北省武邑中学2017-2018学年高二上学期期末考试数学(理)试题
10 . 如图,在棱柱
中,侧棱
底面
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572928027140096/1572928033464320/STEM/b05b03fe-eddd-4d39-acda-c9182dbe7fe0.png)
(1)求证:
平面
;
(2)求直线
与平面
所成的角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44242282970702c5ddfe3e812c533647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ded7fda1dd77ece5897babd6285145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572928027140096/1572928033464320/STEM/b05b03fe-eddd-4d39-acda-c9182dbe7fe0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2016-12-04更新
|
950次组卷
|
4卷引用:2015-2016学年河北省武邑中学高一下期中数学试卷
2015-2016学年河北省武邑中学高一下期中数学试卷安徽省阜阳市太和第一中学2020-2021学年高二(平行班)上学期开学考试数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP357】【数学】湖北省武汉中学2020-2021学年高二上学期期中数学试题