1 . 如图,在棱长为
的正方体
中,点
是棱
的中点,点
在棱
上,且满足
.
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571591338311680/1571591343652864/STEM/75d2bbccc4ae4ec18050cac1fd243dc3.png)
(1)求证:
;
(2)在棱
上确定一点
,使
、
、
、
四点共面,并求此时
的长;
(3)求平面
与平面
所成二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8456cee87c4e22351affc28f3a73a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b74e3ad474d589ef154dbcda5caaa17.png)
![](https://img.xkw.com/dksih/QBM/2014/3/31/1571591338311680/1571591343652864/STEM/75d2bbccc4ae4ec18050cac1fd243dc3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed33744c92e7600d4f2642ec0892560.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fec5bd77cfc1313bc200480cc66c766.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2 . 如图,在三棱柱ABC﹣A1B1C1中,∠BAC=90°,AB=AC=2,AA1=4,A1在底面ABC的射影为BC的中点E,D是B1C1的中点.
![](https://img.xkw.com/dksih/QBM/2016/3/11/1572532911251456/1572532917149696/STEM/e6e568d68d4442409511d2ff8abede5d.png)
(1)证明:A1D⊥平面A1BC;
(2)求点B到平面A1ACC1的距离.
![](https://img.xkw.com/dksih/QBM/2016/3/11/1572532911251456/1572532917149696/STEM/e6e568d68d4442409511d2ff8abede5d.png)
(1)证明:A1D⊥平面A1BC;
(2)求点B到平面A1ACC1的距离.
您最近一年使用:0次
3 . 如图,三角形
是边长为4的正三角形,
底面
,
,点
是
的中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497839104/STEM/ffe287c408e04d25895a9ac9b7693649.png)
(1)证明:平面
平面
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551e4cd76a93de89ea2750160fe74923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4014edd5ca7ddd954507ab87eb2638e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/535a65c61f47d2b893706d4bc3499e20.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497839104/STEM/ffe287c408e04d25895a9ac9b7693649.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d85c98d07c0abe66dc7a529f0dcb14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
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4 . 如图,三角形△PDC所在的平面与长方形ABCD所在的平面垂直,PD=PC=4,AB=6,BC=3,点E是CD的中点,点F、G分别在线段AB、BC上,且AF=2FB,CG=2GB.
(1)证明:PE⊥FG;
(2)求二面角P﹣AD﹣C的正切值;
(3)求直线PA与直线FG所成角的余弦值.
您最近一年使用:0次
2016-12-03更新
|
4745次组卷
|
4卷引用:2015年全国普通高等学校招生统一考试理科数学(广东卷)
2015年全国普通高等学校招生统一考试理科数学(广东卷)四川省宜宾县第二中学校2017-2018学年高一下学期期末模拟数学试题(已下线)专题23 立体几何解答题(理科)-1专题30立体几何与空间向量解答题(第一部分)
12-13高二上·广东梅州·期末
5 . 如图正方体ABCD-
中,E、F、G分别是
、AB、BC的中点.
(1)证明:
⊥平面AEG;
(2)求
,![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/361ecb64299d4e038ee9985b012b7140.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/289a500d10474c9cb90e1f9405415070.png?resizew=62)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/dda4d0cee1974a3998bece70cd3586a1.png?resizew=29)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/0ff6e007c8664ee097974085ee16481e.png?resizew=32)
(2)求
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/1b65aa56036a434bb9100479b88dd19d.png?resizew=65)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/361ecb64299d4e038ee9985b012b7140.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2012/2/15/1570739834798080/1570739840245760/STEM/c44a38897617417690cee742c5d653c5.png?resizew=124)
您最近一年使用:0次
12-13高二上·黑龙江大庆·开学考试
6 . 如图
,在三棱锥
中,
平面
,
,
为侧棱
上一点,它的正(主)视图和侧(左)视图如图
所示.
(
)证明:
平面
.
(
)求三棱锥
的体积.
(
)在
的平分线上确定一点
,使得
平面
,并求此时
的长.
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/6ef207b0e144411795bfccdf8bb1b3d1.png?resizew=133)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e258c6995b058164df335e154692b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/6ef207b0e144411795bfccdf8bb1b3d1.png?resizew=133)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/1041d663056042889cc4a4a01e46ed8a.png?resizew=234)
您最近一年使用:0次
2016-12-02更新
|
1497次组卷
|
8卷引用:2012-2013学年广东省揭阳一中高一下学期第一次段考文科数学试卷
(已下线)2012-2013学年广东省揭阳一中高一下学期第一次段考文科数学试卷(已下线)2012-2013学年黑龙江大庆实验中学高二上学期开学考试文科数学试卷(已下线)2012-2013学年湖北武汉部分重点中学高二上学期期末考试文科数学卷北京市海淀清华附永丰学校2016-2017学年高二上学期期中考试数学试题(已下线)专题46 空间向量与立体几何大题解题模板-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题46 空间向量与立体几何大题解题模板-2021年高考一轮数学(理)单元复习一遍过(已下线)专题43 立体几何大题解题模板-2021年高考一轮数学(文)单元复习一遍过(已下线)专题03 立体几何大题解题模板-(新教材)2020-2021学年高二数学单元复习(人教A版选择性必修第一册)
2012·浙江台州·二模
名校
7 . 如图,AC是圆O的直径,点B在圆O上,∠BAC=30°,BM⊥AC交AC于点M,EA⊥平面ABC,FC//EA,AC=4,EA=3,FC=1.
(1)证明:EM⊥BF;
(2)求平面BEF与平面ABC所成的二面角的余弦值.
(1)证明:EM⊥BF;
(2)求平面BEF与平面ABC所成的二面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2012/7/30/1570943890194432/1570943895568384/STEM/5e458b96-13c1-4413-af71-836dc330dd33.png?resizew=146)
您最近一年使用:0次
2016-12-01更新
|
1376次组卷
|
9卷引用:广东省广州市第二中学高二上学期数学人教A版选修2-1模块测试试卷
广东省广州市第二中学高二上学期数学人教A版选修2-1模块测试试卷(已下线)2012届浙江省台州中学高三下学期第二次统练文科数学(已下线)2012届浙江省宁波市五校高三适应性考试理科数学试卷(已下线)2012届浙江省东阳中学高三5月模拟考试理科数学试卷(已下线)2014届浙江省绍兴市第一中学高三上学期回头考试理科数学试卷2016届海南省文昌中学高三上学期期末考试理科数学试卷2017届陕西师范大学附属中学高三上学期第二次模考数学(理)试卷陕西省西安市长安区第一中学2017届高三4月模拟考试数学(理)试题2018届高三数学训练题:阶段滚动检测试题(六)
8 . 已知梯形
所在平面垂直于平面
于
,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572977096335360/1572977102618624/STEM/9526aab3260a4afca442a492004ee0b1.png)
(1)求证:
;
(2)求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2bfa3d38d79fec4ad193aded145d364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba598b9c579ca748a0232727e19d8182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9eadc2feca23f49e36ade66f66512e1.png)
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572977096335360/1572977102618624/STEM/9526aab3260a4afca442a492004ee0b1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98db3820190babd3569a7e724bb0bc7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
您最近一年使用:0次
11-12高二上·广东·期中
名校
解题方法
9 . 如图,在三棱锥P﹣ABC中,E,F分别为AC,BC的中点.
(1)求证:EF∥平面PAB;
(2)若平面PAC⊥平面ABC,且PA=PC,∠ABC=90°,求证:平面PEF⊥平面PBC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/00199af2-9023-45c7-afc6-8b6f3d2bf55e.png?resizew=158)
(1)求证:EF∥平面PAB;
(2)若平面PAC⊥平面ABC,且PA=PC,∠ABC=90°,求证:平面PEF⊥平面PBC.
您最近一年使用:0次
2016-12-04更新
|
599次组卷
|
9卷引用:2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷
(已下线)2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷(已下线)2011-2012学年福建省福安一中高一下学期第一次月考数学试卷(已下线)2011-2012学年江西省会昌中学高一下学期第二次月考文科数学试卷2015-2016学年湖南省邵阳市邵东县高一上学期期末数学试卷(已下线)2018年11月25日 《每日一题》人教必修2-每周一测浙江省嘉兴市南湖区第一中学2019-2020学年高二上学期期中数学试题山东省泰安市2020-2021学年高一下学期期末数学试题山东省东营市广饶县第一中学三校区2022-2023学年高二9月月考数学试题山东省临沂市蒙阴县第一中学2022-2023学年高一下学期第二次月考数学试题
10 . 如图所示,四边形ABCD是菱形,O是AC与BD的交点,SA⊥平面ABCD
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526348410880/1572526353981440/STEM/93f3aaa998b54c09979319075893db33.png)
(Ⅰ)求证:平面SAC⊥平面SBD;
(Ⅱ)若∠DAB=120°,DS⊥BS,AB=2,求SO的长及点A到平面SBD的距离.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572526348410880/1572526353981440/STEM/93f3aaa998b54c09979319075893db33.png)
(Ⅰ)求证:平面SAC⊥平面SBD;
(Ⅱ)若∠DAB=120°,DS⊥BS,AB=2,求SO的长及点A到平面SBD的距离.
您最近一年使用:0次