名校
解题方法
1 . 已知正方体
的棱长为
为
的中点,
为
所在平面上一动点,
为
所在平面上一动点,且
平面
,则下列命题正确为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59641403064c08e0011414ccdfb85377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ab6fd9972d6298ae91e81cb75189a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若![]() ![]() ![]() ![]() |
B.若三棱柱![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() |
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3卷引用:第三章 空间轨迹问题 专题四 立体几何轨迹面积、体积问题 微点2 立体几何轨迹面积、体积问题综合训练【培优版】
(已下线)第三章 空间轨迹问题 专题四 立体几何轨迹面积、体积问题 微点2 立体几何轨迹面积、体积问题综合训练【培优版】山东省临沂市第十九中学2023-2024学年高二下学期第一次质量调研考试数学试题山东省枣庄市第八中学2023-2024学年高二上学期学科素养诊断数学试题
解题方法
2 . 如图所示,在棱长为2的正方体
中,点E是棱
的中点,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/701602c7-e766-4285-a71a-ab28e4bd2d7a.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/701602c7-e766-4285-a71a-ab28e4bd2d7a.png?resizew=163)
A.点![]() ![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.三棱锥![]() |
D.若点M在底面ABCD内运动,且点M到直线![]() ![]() |
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2024-02-04更新
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3卷引用:第三章 空间轨迹问题 专题一 立体几何轨迹常见结论及常见解法 微点3 立体几何轨迹常见结论及常见解法综合训练【培优版】
(已下线)第三章 空间轨迹问题 专题一 立体几何轨迹常见结论及常见解法 微点3 立体几何轨迹常见结论及常见解法综合训练【培优版】山东省济宁市2023-2024学年高二上学期期末质量检测数学试题浙江省2023-2024学年高二下学期3月四校联考数学试题
名校
3 . 如图,点
是棱长为2的正方体
的表面上一个动点,
是线段
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.当直线![]() ![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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3卷引用:第二章 立体几何中的计算 专题六 空间定值问题 微点6 空间定值问题综合训练【培优版】
(已下线)第二章 立体几何中的计算 专题六 空间定值问题 微点6 空间定值问题综合训练【培优版】湖北省部分省级示范高中2023-2024学年高二上学期期末考试数学试题湖北省十一校2024届高三联考考后提升数学模拟训练一
2024高三·全国·专题练习
4 . 如图所示,在棱长为
的正方体
中,
分别为棱
,
的中点,
为侧面
的一动点,下列说法正确的是
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/0b523ef7-bda6-4fa3-b12c-f334e0b6c0ab.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/2024/1/31/3423234318589952/3423372185239552/STEM/e7003939f1d94fa9bb3bad4b3e4813e7.png?resizew=4)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/0b523ef7-bda6-4fa3-b12c-f334e0b6c0ab.png?resizew=160)
A.异面直线![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.过直线![]() ![]() ![]() ![]() ![]() |
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2024高三·全国·专题练习
5 . 如图,在长方体
中,
,
,
为
中点,
为矩形
内的动点
包括边界
,且
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/b5008a7b-5111-42dd-95a9-dc93f21745ef.png?resizew=149)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce08128582a7e855852c03e0ac5d0487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8c94316312f093ebfc80b872a83c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652f27b965cd841d72312d2aab1c0a22.png)
![](https://img.xkw.com/dksih/QBM/2024/1/31/3423234318589952/3423372185886720/STEM/e7003939f1d94fa9bb3bad4b3e4813e7.png?resizew=4)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/b5008a7b-5111-42dd-95a9-dc93f21745ef.png?resizew=149)
A.点![]() |
B.点![]() |
C.点![]() ![]() ![]() ![]() |
D.点![]() ![]() |
您最近一年使用:0次
名校
6 . 已知四棱锥
中,侧面
底面
,
,底面
是边长为
的正方形,
是四边形
及其内部的动点,且满足
,则动点
构成的区域面积为( )
![](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/643576db3f15492e24e8f32bab2121fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78734399ecec0ab59be485538e816060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-31更新
|
684次组卷
|
3卷引用:北京市平谷区2023-2024学年高二上学期期末教学质量监控数学试卷
名校
解题方法
7 . 类似平面解析几何中的曲线与方程,在空间直角坐标系中,可以定义曲面(含平面)
的方程,若曲面
和三元方程
之间满足:①曲面
上任意一点的坐标均为三元方程
的解;②以三元方程
的任意解
为坐标的点均在曲面
上,则称曲面
的方程为
,方程
的曲面为
.已知曲面
的方程为
.
过曲面
上一点
,以
为方向向量,求证:直线
在曲面
上(即
上任意一点均在曲面
上);
(2)已知曲面
可视为平面
中某双曲线的一支绕
轴旋转一周所得的旋转面;同时,过曲面
上任意一点,有且仅有两条直线,使得它们均在曲面
上.设直线
在曲面
上,且过点
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa13f27f92b55bd7ecd9d750f98ae99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd047376c4cf1b9992cd8e4fe20df2.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/33d7a5b312e3d789a1070000315d63b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b4e60b50889c152c56fcf2d6ea35bc.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知曲面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ddad9072eb1393ce15ca0627c941b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
您最近一年使用:0次
解题方法
8 . 在正方体
中,
,点
在底面正方形
内及边界上运动,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.存在点![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
9 . 在三棱锥
中,
平面
,
,
是底面
上(含边界)的一个动点,
是三棱锥
的外接球
表面上的一个动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df424b9f2699c537962aab7659b5b715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.当![]() ![]() ![]() |
B.![]() |
C.当![]() ![]() ![]() ![]() |
D.存在点![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
10 . 正方体
中,
为
的中点,
为正方体表面上一个动点,则( )
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.当![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-22更新
|
324次组卷
|
3卷引用:河北省石家庄市部分重点高中2023-2024学年高三上学期2月期末数学试题
河北省石家庄市部分重点高中2023-2024学年高三上学期2月期末数学试题(已下线)2024年高考数学二轮复习测试卷(新高考Ⅰ卷专用)广东省深圳外国语学校、执信中学2023-2024学年高三上学期期末校际联考数学试卷