名校
1 . 如图,在圆台
中,
分别为上、下底面直径,且
,
,
为异于
的一条母线.
为
的中点,证明:
平面
;
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601050d23e9d0b81ee6c5eda991dbdf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86605a29fe8fff454e0db6b86047a8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afabf56cc68ea438a890f9fea04b708e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc9e0457471047bc750ecd31989414a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6647d7d03d64dc6eac2c9651badd9376.png)
您最近一年使用:0次
2023-03-29更新
|
5589次组卷
|
14卷引用:江苏省八市(南通、泰州、扬州、徐州、淮安、连云港、宿迁、盐城)2023届高三二模数学试题
江苏省八市(南通、泰州、扬州、徐州、淮安、连云港、宿迁、盐城)2023届高三二模数学试题重庆市缙云教育联盟2023届高三二模数学试题江苏省八市2023届高三下学期第二次调研测试数学试题2024届安徽省阜阳市皖江名校联盟高三模拟预测数学试题(已下线)专题07立体几何的向量方法(已下线)押新高考第20题 立体几何(已下线)江苏省八市2023届高三二模数学试题变式题17-22专题16空间向量与立体几何(解答题)江苏省部分四星级高中2023-2024学年高三上学期期初调研数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期期初调研数学试题广东省湛江市第一中学2023-2024学年高二上学期第一次大考数学试题江苏省镇江市扬中市第二高级中学2023-2024学年高三上学期期末模拟数学试题3(已下线)空间向量与立体几何江苏省南京外国语学校2023-2024学年高三上学期期中模拟数学试题
2 . 将两个各棱长均为1的正三棱锥
和
的底面重合,得到如图所示的六面体,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
A.该几何体的表面积为![]() |
B.该几何体的体积为![]() |
C.过该多面体任意三个顶点的截面中存在两个平面互相垂直 |
D.直线![]() ![]() |
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2024-03-25更新
|
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3卷引用:湖北省武汉市2024届高中毕业班二月调研考试数学试题
名校
解题方法
3 . 在
中,
,过点
作
,交线段
于点
(如图1),沿
将
折起,使
(如图2),点
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/af1034bc-5ab5-4b98-9116-da4bc36f5d26.png?resizew=378)
(1)求证:
;
(2)在①图1中
,②图1中
,③图2中三棱锥
的体积最大.
这三个条件中任选一个,补充在下面问题中,再解答问题.
问题:已知__________,试在棱
上确定一点
,使得
,并求平面
与平面
的夹角的余弦值.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16770045e02c32c6b246f1e88c580647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1347b1707478d309af4287a00e852b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5889e1f093f2c35273d3132ef8434e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cca04b2a2b61d62a809776670a60c09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/af1034bc-5ab5-4b98-9116-da4bc36f5d26.png?resizew=378)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73038c8fab9ef31d42b3ee0631b3dd1c.png)
(2)在①图1中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e84ed4d1ef85e452a30c6b8f7981b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1371c97ec3d0ea7b3ef979f5538d330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
这三个条件中任选一个,补充在下面问题中,再解答问题.
问题:已知__________,试在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5448218bd8c5b4f4a3714e0b0292d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5ce42fe8ea626c297e3b2a2ab95149.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2023-03-28更新
|
1239次组卷
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6卷引用:湖南省岳阳市2023届高三下学期二模数学试题
湖南省岳阳市2023届高三下学期二模数学试题四川省内江市2023届高三第三次模拟考试数学(理科)试题(已下线)专题07立体几何的向量方法专题16空间向量与立体几何(解答题)宁夏银川一中2022-2023学年高二下学期期中考试数学(理)试题(已下线)专题06 立体几何 第一讲 立体几何中的证明问题(分层练)
4 . 将正方形
绕直线
逆时针旋转
,使得
到
的位置,得到如图所示的几何体.
平面
;
(2)点
为
上一点,若二面角
的余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6380f35cdd3050759a4a91b8637adc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb53e0fdf3ebeb96e4f69feacbd80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a903891e53a9b7768e1c5ae7126f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94d2506539ad8760cf7ed366c0c537c.png)
您最近一年使用:0次
名校
5 . 双曲抛物线又称马鞍面,其形似马具中的马鞍表面而得名.其在力学、建筑学、美学中有着广泛的应用.在空间直角坐标系中,将一条
平面内开口向上的抛物线沿着另一条
平面内开口向下的抛物线滑动(两条抛物线的顶点重合)所形成的就是马鞍面,其坐标原点被称为马鞍面的鞍点,其标准方程为
,则下列说法正确的是()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1e8a88d934eca5399decc64fdbd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263f7c17b63a6c59bbfd4f68d6023cf6.png)
A.用平行于![]() |
B.用法向量为![]() |
C.用垂直于y轴的平面截马鞍面所得轨迹为双曲线 |
D.用过原点且法向量为![]() |
您最近一年使用:0次
2024-02-27更新
|
872次组卷
|
8卷引用:第6套 重组模拟卷(模块二 2月开学)
(已下线)第6套 重组模拟卷(模块二 2月开学)河南省郑州市宇华实验学校2024届高三下学期第二次模拟考试数学试题2024届江苏省南京师范大学附属扬子中学高三第二次模拟考试数学试卷河北省2024届高三下学期大数据应用调研联合测评(V)数学试题河北省沧州市泊头市大数据联考2024届高三下学期2月月考数学试题河北省秦皇岛市昌黎县开学联考2024届高三下学期开学考试数学试题(已下线)高三数学考前冲刺押题模拟卷01(2024新题型)江西省南昌市第二中学等部分学校2024届高三下学期3月联考数学试题
名校
6 . 如图所示的六面体中,
,
,
两两垂直,
连线经过三角形
的重心
,且
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07e98f7a65097311e8d93bd9f2af26e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若点![]() ![]() ![]() |
您最近一年使用:0次
2023-12-20更新
|
770次组卷
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3卷引用:山东省潍坊市2024届高三上学期普通高中学科素养能力测评数学试题
7 . 如图,在正方体
中,
在棱
上,
,平行于
的直线
在正方形
内,点
到直线
的距离记为
,记二面角为
为
,已知初始状态下
,
,则( )
![](https://img.xkw.com/dksih/QBM/2021/5/15/2721736974172160/2724289797496832/STEM/f84fcd4b-2e4f-49be-8965-2ea8f30191ea.png?resizew=260)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a666403569e607f32af5f762c246dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6fc4f2fb4cb73db222591261f2d7bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fa64abb0036dbff6a29f01b0c03899.png)
![](https://img.xkw.com/dksih/QBM/2021/5/15/2721736974172160/2724289797496832/STEM/f84fcd4b-2e4f-49be-8965-2ea8f30191ea.png?resizew=260)
A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
您最近一年使用:0次
2021-05-19更新
|
2666次组卷
|
9卷引用:浙江省数海漫游2021届高三下学期第二次模拟考试数学试题
浙江省数海漫游2021届高三下学期第二次模拟考试数学试题浙江省2022届高三下学期高考冲刺卷(一)数学试题(已下线)考向36 立体几何中的向量方法(已下线)专题9.立体几何与空间向量 -《2022届复习必备-2021届浙江省高考冲刺数学试卷分项解析》(已下线)考点35 立体几何中的综合问题-备战2022年高考数学典型试题解读与变式(已下线)专题23 立体几何中的压轴小题-2(已下线)第一章 空间向量与立体几何(压轴题专练,精选20题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)专题14 立体几何常见压轴小题全归纳(9大核心考点)(讲义)(已下线)第二章 立体几何中的计算 专题二 空间距离 微点1 两点间的距离、点到直线的距离【基础版】
8 . 如图,已知圆柱的上,下底面圆心分别为
是圆柱的轴截面,正方形ABCD内接于下底面圆Q,
.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877184706306048/2916904990130176/STEM/69f5bc23f7314f5c8dabf6d4b54890aa.png?resizew=126)
(1)当k为何值时,点Q在平面PBC内的射影恰好是△PBC的重心;
(2)若
,当平面PAD与平面PBC所成的锐二面角最大时,求该锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54840995c545df777ab9196813ddc5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667206277277c8a79bd370cb167a6acd.png)
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877184706306048/2916904990130176/STEM/69f5bc23f7314f5c8dabf6d4b54890aa.png?resizew=126)
(1)当k为何值时,点Q在平面PBC内的射影恰好是△PBC的重心;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad013ed89855a7f3c795c48bc7c91f1.png)
您最近一年使用:0次
2022-02-15更新
|
1304次组卷
|
2卷引用:山东省潍坊市2021-2022学年高三上学期学科核心素养测评数学试题
9 . 三棱锥
中,
平面
,
,
,并且
是直角.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/00c24e80-c7c0-456e-97a3-6fe819ef484d.png?resizew=175)
(1)求二面角
所成角的余弦值;
(2)若
,
,
上各取一点
,
,设
(
),当
为何值时,平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535bfd65eb04a29d64425d54b2acf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c184f8272d86497134b0bc225c8645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/00c24e80-c7c0-456e-97a3-6fe819ef484d.png?resizew=175)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b787fcc1da13b8665a7d6a41a75328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0639327721a50d83bee4fdc44a9c468f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.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/6fc981f1af8f5e82d51da9e6f139c177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
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10 . 在圆柱
中,等腰梯形
为底面圆
的内接四边形,且
,矩形
是该圆柱的轴截面,
为圆柱的一条母线,
.
(1)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42cb320b4c1333296d5c5eca549f304.png)
平面
;
(2)设
,
,试确定
的值,使得直线
与平面
所成角的正弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c0ee0aca57a218e5612835ab49ee2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21093eae7765f54a8de66750a63e1a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/5/f7290855-b1f2-4b9d-ad7b-7b801e04eea2.png?resizew=164)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42cb320b4c1333296d5c5eca549f304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0515adff91b7ab39e9e1fb88943ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29837db4ec4d0aeb8d7ad9fcb316d6.png)
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