名校
1 . 下列命题为真命题的是( )
A.已知a、b、c、d是空间中的四条不同直线,若![]() ![]() |
B.已知a、b是两条直线,![]() ![]() ![]() ![]() |
C.已知m、n是两条空间直线,![]() ![]() ![]() |
D.已知AB、CD是平面![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022高三·全国·专题练习
解题方法
2 . 如图,在棱长为2的正方体
中,
,
分别是棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890852519501824/2893539640451072/STEM/095f9190ca394bbd806b306474b6f8ac.png?resizew=202)
(1)求异面直线
与
所成角的大小;
(2)连接
,与
交于点
,点
在线段
上移动.求证:
与
保持垂直;
(3)已知点
是直线
上一点,过直线
和点
的平面交平面
于直线
,试根据点
的不同位置,判断直线
与直线
的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890852519501824/2893539640451072/STEM/095f9190ca394bbd806b306474b6f8ac.png?resizew=202)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
您最近一年使用:0次
名校
3 . 已知异面直线
所成角的大小为
,直线
且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2979f64c85f82d8975d73ee1c342de.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6340b8c5618b64a78e83fe4ab075f0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ddbceabfc3d02a6b6b921f6bf5b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2979f64c85f82d8975d73ee1c342de.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,已知四边形
是矩形,
平面
,且
,M、N是线段
、
上的点,满足
.
![](https://img.xkw.com/dksih/QBM/2022/5/5/2972618227073024/2974405463597056/STEM/c06c52a6-d20a-4595-b1e4-f7fd14690d17.png?resizew=189)
(1)若
,求证:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)是否存在实数
,使直线
同时垂直于直线
,直线
?如果有请求出
的值,否则请说明理由;
(3)若
,求直线
与直线
所成角的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cbd23176d1f96deb84372973e16a63.png)
![](https://img.xkw.com/dksih/QBM/2022/5/5/2972618227073024/2974405463597056/STEM/c06c52a6-d20a-4595-b1e4-f7fd14690d17.png?resizew=189)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
您最近一年使用:0次
2022-05-07更新
|
404次组卷
|
3卷引用:上海市控江中学2021-2022学年高二下学期期中数学试题
上海市控江中学2021-2022学年高二下学期期中数学试题第10章 空间直线与平面(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020必修第三册)(已下线)10.3 直线与平面所成的角 (第4课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020必修第三册)
5 . 记正方体
的八个顶点组成的集合为
.若集合
,满足
,
,
,
使得直线
,则称
是
的“保垂直”子集.
给出下列三个结论:
①集合
是
的“保垂直”子集;
②集合
的含有6个元素的子集一定是“保垂直”子集;
③若
是
的“保垂直”子集,且
中含有5个元素,则
中一定有4个点共面.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550891fd3592f36b53257ec8052f7450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f40413bb494d324127748478cb7ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56048afc8e7c0ef7c817aea6bfb22b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf3ac8b2128ec97cbced53f0438c085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56294f5024f1f83182b3d0ee0dab42ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e28ac4ec68ec9d8096c08af468429c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
给出下列三个结论:
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afed0c3ca9fe1af74bf50cdf0bf6a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
6 . 若平面
的斜线l在
内的射影为
,直线
,且
,则b与l( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b330d69a949d9b55f4b6f18f47e0a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4751b438a4abc833bcb1909dd7d82027.png)
A.必相交 | B.必为异面直线 | C.垂直 | D.平行 |
您最近一年使用:0次
解题方法
7 . 已知
分别是圆柱
上、下底面圆的圆心,
分别是上、下底面圆周上一点,若
,且直线
与
垂直,则直线
与
所成的角的正切值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c8e67ae6659fb77dc4e33154e4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bea5e9441f29e640664c0e68c1788b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd37244e07a7f1e6b0d8afdb469cf76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
8 . 在“立体几何”知识中:①两直线所成角的取值范围是
;②直线与平面所成角的取值范围是
;③二面角的平面角取值范围是
.在“解析几何”知识中;④直线的倾斜角取值范围是
;⑤两直线的夹角取值范围是
;在“向量”知识中:⑥两向量的夹角的取值范围是
;以上概念叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa898d5280ab56f52aeedc2cce370bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14bdd7f2b48c0ce6ba8696c89fbf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b1d28a098ea5555c89b332fad25b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917ae6fcf56fa6b4fc9852854cd8f78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
A.②①④⑤ | B.②③④⑥ | C.③④⑤⑥ | D.②③④⑤ |
您最近一年使用:0次
解题方法
9 . 如图,已知椭圆
的长轴端点为
,
,短轴端点为
,
,焦点为
,
.现将左边半个椭圆沿短轴进行翻折,则在翻折过程中(不共面),以下说法不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/288eec6e-1680-4267-8159-88e8a892996a.png?resizew=206)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/288eec6e-1680-4267-8159-88e8a892996a.png?resizew=206)
A.存在某个位置,使![]() |
B.存在某个位置,使二面角![]() ![]() |
C.对任意位置,都有![]() ![]() |
D.异面直线![]() ![]() ![]() |
您最近一年使用:0次
2021-11-06更新
|
623次组卷
|
7卷引用:浙江省2022届高考模拟卷数学试题(二)
浙江省2022届高考模拟卷数学试题(二)(已下线)考点31 直线、平面平行与垂直的判定与性质-备战2022年高考数学典型试题解读与变式(已下线)考点38 椭圆-备战2022年高考数学典型试题解读与变式(已下线)热点09 解析几何-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)考向32 椭圆(重点)河南省驻马店市上蔡县衡实中学2022-2023学年高二上学期11月期中考试理科数学试题(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点7 圆锥曲线中的翻折问题(二)
10 . 已知点
为正方体
内(含表面)的一点,过点
的平面为
,以下描述正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.与![]() ![]() ![]() |
B.过点![]() ![]() ![]() |
C.与正方体的所有棱所成的角都相等的![]() |
D.过点![]() |
您最近一年使用:0次