2021·全国·模拟预测
名校
解题方法
1 . 如图,在正三棱柱
中,点D为棱BC的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882961348149248/2883220302872576/STEM/3dc04c019e1844bbbc2adbbf8d34141e.png?resizew=207)
(1)证明:
;
(2)若点E为棱AB上一点,且满足______,求二面角
的正弦值.
从①
;②
这两个条件中任选一个填入上面的横线上,并解答问题.
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/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882961348149248/2883220302872576/STEM/3dc04c019e1844bbbc2adbbf8d34141e.png?resizew=207)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06769ce64b9bc0a23ead087fc7f8c55e.png)
(2)若点E为棱AB上一点,且满足______,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c07c2e932d60994bd58a04dd193f39.png)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176a1127a464fed085df602e1e235c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d382176514c5da39e93a8e15cf4e2f74.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
名校
2 . 如图,四边形
是边长为
的正方形,点
、
分别为线段
、
上的动点,
,将
翻折成
,且平面
平面
,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/12/9/2868672375586816/2868993859608576/STEM/f6501e57d18145d491c01386892afa27.png?resizew=340)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a3600b1760a63a10c9a0429b439dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae27598851148e664c4af461f539356e.png)
![](https://img.xkw.com/dksih/QBM/2021/12/9/2868672375586816/2868993859608576/STEM/f6501e57d18145d491c01386892afa27.png?resizew=340)
A.存在点![]() ![]() |
B.当点![]() ![]() ![]() ![]() |
C.三棱锥![]() ![]() ![]() |
D.存在点![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 下图是常见的一种灭火器消防箱,抽象成数学模型如右图所示的六面体,其中四边形
和
为直角梯形,A、D、C、B为直角顶点,其他四个面均为矩形,
,
,
,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844066014797824/2844861979435008/STEM/2c2e393edda84a1c915e359689ad878e.png?resizew=115)
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844066014797824/2844861979435008/STEM/b3a63a66602f43fdb1626ea52290071d.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6895631698282a5e8887a09177cc98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60c3b75ff1610956dfe9a9cd7692d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d86096d3211fc58450eb7b02899b554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cec73fce3ed065803d763c700124a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844066014797824/2844861979435008/STEM/2c2e393edda84a1c915e359689ad878e.png?resizew=115)
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844066014797824/2844861979435008/STEM/b3a63a66602f43fdb1626ea52290071d.png?resizew=171)
A.该几何体是四棱台 |
B.该几何体是棱柱,面![]() |
C.![]() |
D.面![]() ![]() |
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名校
4 . 已知圆锥的顶点为
,圆锥底面圆心为
,
是底面的一条直径,且
,
为底面圆周上一动点(不与
,
重合).
(1)设
的中点为
,求证:
平面
;
(2)二面角
是否可能为直角?若是,求
的位置;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/7b4cc22a5ec7ffd4dd8035dad0b6bb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad799526cb79a35faf53974af034c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b312de408dda638ca3e9c687549d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2021-10-15更新
|
315次组卷
|
3卷引用:天墟观2021-2022学年度高三上学期模拟(新高考)数学试题(二)
名校
解题方法
5 . 如图,在圆锥
中,
的内接
为等边三角形,
,且圆锥的侧面展开图恰好为半圆.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/4d01a870-469a-4995-8e97-10d83ce2db30.png?resizew=157)
(1)证明:
;
(2)点
是底面
上的一个动点,
,求二面角
余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/4d01a870-469a-4995-8e97-10d83ce2db30.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7c18f9db65fcd840b39d7bbd3028c.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cb74a4c5de601b57b2cb45ecd1cf5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486aa57b8d51f4bafedf8b31ed0b6452.png)
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6 . 已知二面角
的平面角为
,平面
的一个法向量为
,平面
的一个法向量为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ee2894ba8c5cee6633430cc8b3b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2021-08-31更新
|
686次组卷
|
5卷引用:福建省福清西山学校2021-2022学年高二9月月考数学试题
福建省福清西山学校2021-2022学年高二9月月考数学试题湖北省武汉市第十四中学2021-2022学年高二上学期10月月考数学试题沪教版(2020) 选修第一册 同步跟踪练习 第3章 3.3~3.4 阶段综合训练(已下线)第04讲 空间向量的应用(4大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)广东省普宁市2019-2020学年高二上学期期中数学试题
7 . 如图所示,设正方体
的棱长为1,
是棱
的中点,一只蚂蚁从
点出发,沿该正方体的表面直线型爬行一圈,蚂蚁首先爬到点
,然后在上底面
爬行,再在右侧面爬行到点
,最后沿
回到起点
,蚂蚁爬行一圈的封闭路径正好在平面
内.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/a526de9a-9fef-41b8-8a4c-b2fe19732974.png?resizew=180)
(1)求证:蚂蚁在上底面
上爬行的路线
与
平行;
(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/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/a526de9a-9fef-41b8-8a4c-b2fe19732974.png?resizew=180)
(1)求证:蚂蚁在上底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
8 . 如图1,菱形
中
,动点
,
在边
,
上(不含端点),且存在实数
使
,沿
将
向上折起得到
,使得平面
平面
,如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/ac397c0a-4757-41ae-8f7c-fb0aef905b3b.png?resizew=335)
(1)若
,设三棱锥
和四棱锥
的体积分别为
,
,求
;
(2)试讨论,当点
的位置变化时,二面角
是否为定值,若是,求出该二面角的余弦值,若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c23ebae33b63bc041229cc7d7c0d97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae27598851148e664c4af461f539356e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/12/ac397c0a-4757-41ae-8f7c-fb0aef905b3b.png?resizew=335)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d23f34a0d1095678f4532f2a7f4c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901a2782695f963fe55a1aeaacb927c7.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/f737b04ce09bc7e1ed86dc9b3c85203b.png)
(2)试讨论,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f33997d5b4a0d9a3feafc1a075bc56.png)
您最近一年使用:0次
2021-06-03更新
|
2515次组卷
|
12卷引用:重庆市蜀都中学2021届高三下学期4月月考数学试题
重庆市蜀都中学2021届高三下学期4月月考数学试题重庆市南开中学2021届高三下学期第六次质量检测数学试题(已下线)考点突破11 空间向量与立体几何-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)第一章 空间向量与立体几何单元检测(能力挑战卷)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)重庆市蜀都中学2021届高三下学期三月月考数学试题(已下线)1.4 空间向量的应用-2021-2022学年高二数学同步速效提升练(人教A版2019选择性必修第一册)【学科网名师堂】(已下线)专题04 二面角(含探索性问题)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)(已下线)2021年新高考浙江数学高考真题变式题17-22题(已下线)第一章 空间向量与立体几何 章末测试(提升)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)四川省遂宁市安居育才中学校2022-2023学年高二上学期期末数学(理)试题(已下线)高二上学期期中【易错60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)(已下线)模块二 专题1《空间向量与立体几何》单元检测篇 B提高卷(人教A)
9 . 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)
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A.当![]() ![]() | B.当![]() ![]() |
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2021-05-19更新
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2654次组卷
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9卷引用:考向36 立体几何中的向量方法
(已下线)考向36 立体几何中的向量方法(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】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(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》浙江省2022届高三下学期高考冲刺卷(一)数学试题
名校
解题方法
10 . 如图,在水平桌面上放置一块边长为
的正方形薄木板
.先以木板的
边为轴,将木板向上缓慢转动,得到平面
,此时
的大小为
.再以木板的
边为轴,将木板向上缓慢转动,得到平面
,此时
的大小也为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8d53e369-4880-45b2-8a15-ae5ee78362d4.png?resizew=216)
(1)求整个转动过程木板扫过的体积;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c73b73825032f9c9721e5ba1efc6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7034291c5bd186735e75f11cf0cd14cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc5bb66927b8843c69771bd277c0123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672c9e8f85f74ed6570425835389fd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a1ec4e35c3565eeaf0144b63beb86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8d53e369-4880-45b2-8a15-ae5ee78362d4.png?resizew=216)
(1)求整个转动过程木板扫过的体积;
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672c9e8f85f74ed6570425835389fd55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2021-04-30更新
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294次组卷
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3卷引用:专题3.6 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)
(已下线)专题3.6 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)江苏省六校2021届高三下学期第四次适应性联考数学试题江西省鹰潭市贵溪市第一中学2024届高三上学期期中考试数学试题