解题方法
1 . 蜂巢是由工蜂分泌蜂蜡建成的从正面看,蜂巢口是由许多正六边形的中空柱状体连接而成,中空柱状体的底部是由三个全等的菱形面构成,菱形的一个角度是
,这样的设计含有深刻的数学原理、我国著名数学家华罗庚曾专门研究蜂巢的结构著有《谈谈与蜂房结构有关的数学问题》.用数学的眼光去看蜂巢的结构,如图,在六棱柱
的三个顶点A,C,E处分别用平面BFM,平面BDO,平面DFN截掉三个相等的三棱锥
,
,
,平面BFM,平面BDO,平面DFN交于点P,就形成了蜂巢的结构.如图,设平面PBOD与正六边形底面所成的二面角的大小为
,则有:( )
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445439580864512/2447861094457344/STEM/e20a3530-a6ad-4f11-9d52-8ad19a19e2a6.png?resizew=208)
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445439580864512/2447861094457344/STEM/b8faa1c6-7eca-4138-a583-894320e10486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a433496bdfa5e0a4a9dd9db0bd3e9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b5b38aa6102f57706113f083a10688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aede171b1554a3a945fefc3c122f900a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce657e1534daf6c5e163895549a47c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f236b9f7b46ba33af145306f421173ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445439580864512/2447861094457344/STEM/e20a3530-a6ad-4f11-9d52-8ad19a19e2a6.png?resizew=208)
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445439580864512/2447861094457344/STEM/b8faa1c6-7eca-4138-a583-894320e10486.png)
A.![]() | B.![]() |
C.![]() | D.以上都不对 |
您最近一年使用:0次
名校
2 . 正方体中
,过
作直线
,若直线
与平面
中的直线所成角的最小值为
,且直线
与直线
所成角为
,则满足条件的直线
的条数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2020-02-05更新
|
1229次组卷
|
3卷引用:浙江省嘉兴市2019-2020学年高二上学期期末数学试题
名校
3 . 如图,
的棱长为1的正方体,任作平面
与对角线
垂直,使得
与正方体的每个面都有公共点,这样得到的截面多边形的面积为
,周长为
的范围分别是_____________ (用集合表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a80427c5520818aa57e4de7bb5ce7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375731341819904/2376091990720512/STEM/d9ef730d-97f3-4a80-8db4-452dadf289e8.png)
您最近一年使用:0次
4 . 在四面体
中,若
,则当四面体
的体积最大时其外接球表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ad6cb5184d5745c51ea56797503d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
5 . 曲线
与过原点的直线
没有交点,则
的倾斜角
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6a0b773da0f3f00408053be915992b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
6 . 在三棱锥
中,
,
,
,记三棱锥
的体积为
,其外接球的体积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
__
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b3706fb266870ab43a2d16e0812fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08aa6fd52f3933cbded9ce8c880b4a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
您最近一年使用:0次
名校
7 . 已知抛物线
(
),点
在
的焦点
的右侧,且
到
的准线的距离是
到
距离的3倍,经过点
的直线与抛物线
交于不同的
、
两点,直线
与直线
交于点
,经过点
且与直线
垂直的直线
交
轴于点
.
(1)求抛物线
的方程和
的坐标;
(2)判断直线
与直线
的位置关系,并说明理由;
(3)椭圆
的两焦点为
、
,在椭圆
外的抛物线
上取一点
,若
、
的斜率分别为
、
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca3be22daa1081710f6c8a39bb44750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47968de4a67d1083d36c173b3d3c2ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf0685aa2108c61b1e8ab48d3d7c4bb.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d2b01f86fb5a373af6b089cf3d891b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623567de59e50e4066c20804e9168ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623567de59e50e4066c20804e9168ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c139977cac26d9dd6acabec625206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2491acadeba63c5df0b87f7326841376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae28d162338771867dc6805f9dc9dfd6.png)
您最近一年使用:0次
名校
8 . 已知单位向量
两两的夹角均为
(
,且
),若空间向量
满足
,
,则有序实数组
称为向量
在“仿射”坐标系
(O为坐标原点)下的“仿射”坐标,记作
,有下列命题:
①已知
,
,则
;
②已知
,
,其中
,则当且仅当
时,向量
的夹角取得最小值;
③已知
,
,则
;
④已知
,
,
,则三棱锥
的表面积
.
其中真命题为________ (写出所有真命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddad20bb28660b1469acdb5440fa072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcadd1781ee9177e9bc76ce48afdd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50774cbd8f44e5cff06dc7ecaa6bf94e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2e0f39e291976fcffd82bd5182c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83fe554772fa28cae4c9233bde930b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4949663ae37a5fa4417edacedd316762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2e0f39e291976fcffd82bd5182c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a712734f9668a5ad80a0c488cd2147e.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8a9bee1b188009aa812754ee06506b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5852b277cf9c452ca1bea838b30290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25325b09595d8e6ebe66e5140323ef8.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268dc3e270189059630d16e1b4ec4bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f158d248d90b3be8a60abfa97f72c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f57f35fbbb5d288691dda630a44961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b9d5aaaceaa3ac514d17fcfefbf9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019c62d43430ababccb0fe08a55c6ec0.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73371f19cb48256d4dcbbab055c2993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e730da293b8ca1e22bf38e6846dc3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed5928e612316d6203f2e39e15d37b7.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d7d036775ba1a4fa27b15cba598f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b84c4fb07ceba134f667619a492bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6cee41ea9f8642ea78f6f6da7b8827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97de2e90bb2bccefe5039c193429cfc.png)
其中真命题为
您最近一年使用:0次
2019-08-17更新
|
2098次组卷
|
10卷引用:2015届福建省泉州一中高三下学期最后一次模拟理科数学试卷
2015届福建省泉州一中高三下学期最后一次模拟理科数学试卷2015-2016学年江西吉安一中高二上第一次段考理科数学卷【全国市级联考】四川省南充市2018届高三第三次联合诊断考试数学理科试题智能测评与辅导[理]-空间向量与立体几何2020届浙江省杭州市高三下学期4月统测模拟数学试题(已下线)专题06 空间向量与立体几何(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)江西省泰和中学2021-2022学年高二上学期第一次段考数学(理)试题沪教版(2020) 选修第一册 精准辅导 第3章 3.3 空间向量的坐标表示福建省福清西山学校2023-2024学年高二上学期9月月考数学试题(已下线)第3章 空间向量及其应用 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
9 . 如图,正四面体ABCD的顶点C在平面α内,且直线BC与平面α所成的角为45°,顶点B在平面α内的射影为O,当顶点A与点O的距离最大时,直线CD与平面α所成角的正弦值等于( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2019-08-16更新
|
1695次组卷
|
4卷引用:空间几何体的三视图、表面积、体积
空间几何体的三视图、表面积、体积(已下线)专题7-2 立体几何压轴小题:角度与动点、体积(讲+练)-1广东省深圳市深圳外国语学校2024届高三上学期第二次模拟测试数学试题(已下线)广东省深圳市深圳外国语学校2024届高三上学期第二次模拟测试数学试题变式题6-10
名校
10 . 在平面直角坐标系
中,已知以点
为圆心的圆过原点
,不过圆心
的直线
与圆
交于
两点,且点
为线段
的中点,
求
的值和圆
的方程:
若
是直线
上的动点,直线
分别切圆
于
两点,求证:直线
恒过定点;
若过点
的直线
与圆
交于
两点,对于每一个确定的
,当
的面积最大时,记直线
的斜率的平方为
,试用含
的代数式表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8386f556bc51e59250b0c91c5bdcd1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2ed1f2b15c9bd6f5139ef6a14a475a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecae6ad8fd8a0178479b0761ba76d391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1c16a5a5d7d97af3abea607200ec72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca520748c8b8d3878fb112a89ada7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdfbe20697f20ef784f70d69ccf2cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
您最近一年使用:0次