1 . 在三棱柱ABC-A1B1C1中,AB=BC=CA=AA1=2,侧棱AA1⊥面ABC,D、E分别是棱A1B1、AA1的中点,点F在棱AB上,且
.
![](https://img.xkw.com/dksih/QBM/2014/2/8/1571505255211008/1571505260961792/STEM/91b8864a5f9e46b69e5a497f21f4c7fd.png)
(Ⅰ)求证:EF∥平面BDC1;
(Ⅱ)求二面角E-BC1-D的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d318ccd750364557b52b8e2fd9e47eb0.png)
![](https://img.xkw.com/dksih/QBM/2014/2/8/1571505255211008/1571505260961792/STEM/91b8864a5f9e46b69e5a497f21f4c7fd.png)
(Ⅰ)求证:EF∥平面BDC1;
(Ⅱ)求二面角E-BC1-D的余弦值.
您最近一年使用:0次
2010·重庆·一模
2 . 本小题满分14分)
过
轴上动点
引抛物线
的两条切线
、
,
、
为切点,设切线
、
的斜率分别为
和
.
![](https://img.xkw.com/dksih/QBM/2012/5/22/1570862820360192/1570862825824256/STEM/1a164e69-fbe1-43f7-8544-0c12a63eb542.png?resizew=179)
(1)求证:
;
(2)求证:直线
恒过定点,并求出此定点坐标;
(3)设
的面积为
,当
最小时,求
的值.
过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://img.xkw.com/dksih/QBM/2012/5/22/1570862820360192/1570862825824256/STEM/1a164e69-fbe1-43f7-8544-0c12a63eb542.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771a2abef658aab00d81a85ac26d9128.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c9b37099ccac90ccedfd2c37f2d95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1171cac748aeec8f46b69ec79fd257.png)
您最近一年使用:0次
3 . 如图,
平面
,
,
,
,
分别为
的中点.
(Ⅰ)求证:
平面ACD;
(Ⅱ)求几何体
的体积;
(Ⅲ)求平面ADE与平面ABC所成锐二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689c065652544780be8b33ae92cbb6d7.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/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29f52897bd8e15c93884d843555bd7b.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
(Ⅱ)求几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd3df0e78cc51865a46aa0ac013bc44.png)
(Ⅲ)求平面ADE与平面ABC所成锐二面角的正切值.
您最近一年使用:0次
解题方法
4 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
,
是
的中点,
是棱
上的点,且
.
(1)求证:平面
底面
;
(2)求二面角
的大小.
![](https://img.xkw.com/dksih/QBM/2016/5/5/1572620670140416/1572620676153344/STEM/fd00d0f79ec3448586c640030f95e2e4.png?resizew=198)
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ec1d702ce59463c2a1fc468f3da5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d018f0f1a40a5e20179f42c1722946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b79bf9d502660aff58cec76863e610.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a773fe6d12311dc321198697eb528ba.png)
![](https://img.xkw.com/dksih/QBM/2016/5/5/1572620670140416/1572620676153344/STEM/fd00d0f79ec3448586c640030f95e2e4.png?resizew=198)
您最近一年使用:0次
5 . 如图,直四棱柱
的底面是菱形,侧面是正方形,
,
是棱
的延长线上一点,经过点
、
、
的平面交棱
于点
,
.
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/7fda4a1188c44aeda07882746816570e.png)
(1)求证:平面
平面
;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/7e1544dce0c6444095e98410d5b144ec.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/ce3817d1de5e40288099e1ef572c5360.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/47d81cbd42f94972a6c5aeec121d0bf5.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/d9fde37bae5845f5a4595fd78741abcd.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/988ead4333684995b20c5cea100aa2dd.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/4d97607f33c845ecb9f5f1560454875c.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/47d81cbd42f94972a6c5aeec121d0bf5.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/f6c1fd55888e474dbad8db5764dfb6b2.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/0bc48b4480474987a7765462a63dbeae.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/a84a0f61e8cd4b9c90600a9e15a99d96.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/7fda4a1188c44aeda07882746816570e.png)
(1)求证:平面
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/9969bda9e7474275933bf29d75e18d5d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/947f9d34a9fa48ab96a395c866eac02f.png)
(2)求二面角
![](https://img.xkw.com/dksih/QBM/2015/7/16/1572184164057088/1572184169996288/STEM/78070565991f48cb85e8392ad5e58341.png)
您最近一年使用:0次
2016-12-03更新
|
827次组卷
|
3卷引用:2015届甘肃省天水市一中高三第五次高考模拟考试理科数学试卷
11-12高二·江西九江·阶段练习
6 . 如图,在三棱台
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/2c2000c9-bef0-4f9f-b160-84cd08b972ff.png?resizew=191)
(Ⅰ)求证:
平面
;
(Ⅱ)若
平面
,
,
,求平面
与平面
所成角(锐角)的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feeb1d761e66157e36a45040ebdce653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/2c2000c9-bef0-4f9f-b160-84cd08b972ff.png?resizew=191)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1333b03f13c3c738a8308d80ceca62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73152c2b4298298c8b81dc16dc21f5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
您最近一年使用:0次
2016-12-03更新
|
4513次组卷
|
20卷引用:2023届甘肃省高考数学模拟试卷(一)
2023届甘肃省高考数学模拟试卷(一)(已下线)2011-2012学年江西省九江一中高二第二次月考理科数学(已下线)2012届安徽省六安市舒城一中高三第四次月考理科数学2015年全国普通高等学校招生统一考试理科数学(山东卷)2014-2015学年河北省正定中学高一下学期期末考试数学试卷2016届江西省临川区一中高三上学期第一次月考理科数学试卷广东省德庆县香山中学2018届高三理科数学第一次模拟试题苏教版高中数学 高三二轮 专题23 立体几何中的向量方法及抛物线 测试(已下线)5.2 直线 平面平行与垂直的判定与性质[理]-《备战2020年高考精选考点专项突破题集》湖北省重点高中联考协作体2018-2019学年高三下学期期中数学(理)试题2020届山东省青岛天龙中学高三第一次模拟考试数学试题辽宁省沈阳市法库县高级中学2020-2021学年高二上学期10月月考数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP362】【数学】(已下线)【新东方】杭州新东方高中数学试卷359(已下线)专练12 空间向量与立体几何综合检测卷(B卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)陕西省汉中市2022届高三下学期教学质量第二次检测考试理科数学试题2023版 湘教版(2019) 选修第二册 过关斩将 第2章 本章复习提升(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项云南省保山市腾冲市第八中学2023-2024学年高二下学期开学考试数学试题(已下线)专题23 立体几何解答题(理科)-2
7 . 已知双曲线
:
的一条渐近线为
,右焦点
到直线
的距离为
.
(1)求双曲线
的方程;
(2)斜率为
且在
轴上的截距大于
的直线
与曲线
相交于
、
两点,已知
,若
证明:过
、
、
三点的圆与
轴相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74febecdeab2c76afebc30f82212fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5d6092f598c7da4796f965e40525a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572067092578304/1572067098656768/STEM/110d3a99204a46279ad99d4c58ff684a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2016-12-03更新
|
1556次组卷
|
3卷引用:2015届甘肃省兰州市高三诊断考试理科数学试卷
8 . 如图,在四棱锥
中,侧面
底面
,底面
为矩形,
,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/2016/6/22/1572786155315200/1572786161614848/STEM/b5dd853c830d487b9a2894ea70688690.png?resizew=221)
(1)求证:
;
(2)若
与平面
所成的角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce965313d0ebce23a3b66ea8366187fe.png)
![](https://img.xkw.com/dksih/QBM/2016/6/22/1572786155315200/1572786161614848/STEM/b5dd853c830d487b9a2894ea70688690.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b87a95accd0dcf9154737859bba2f1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a37874cd284fb1a8c864769ce50c9.png)
您最近一年使用:0次
2016-12-04更新
|
954次组卷
|
2卷引用:2016年甘肃省兰州市高三实战考试理科数学试卷
9 . 如图,在三棱台
中,平面
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854c2d70c17de3b5b94ce4daa4422efa.png)
.
平面
;
(Ⅱ)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d052663101ca930843abd98cbd61c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854c2d70c17de3b5b94ce4daa4422efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41dff1f0a58d3a8a48d720088fcd6aa.png)
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18卷引用:2023届甘肃省高考数学模拟试卷(三)
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