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1 . 已知空间中三点
,设
.
(1)若
,且
,求向量
,
(2)已知向量
与
互相垂直,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caea6c9439ab6a91b850db54b20cf3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a65875499c8f54e2d5421819cf25af.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3361b587b611701daf8078c1b2d8e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3752d53506c02e33cc527391bebbbea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2 . 在下列四个命题中,正确命题的是( )
A.若向量![]() ![]() |
B.向量![]() ![]() ![]() ![]() |
C.直线![]() ![]() |
D.若存在不全为0的实数x,y,z使得![]() ![]() |
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3 . 下列结论中正确的有( )
A.过点![]() ![]() ![]() |
B.过点![]() ![]() ![]() |
C.若直线![]() ![]() ![]() |
D.过点![]() ![]() |
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23-24高二上·江苏南通·阶段练习
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4 . 直线
与直线
相交于点P,对任意实数m,直线
,
分别恒过定点A,B,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1de5bf2aa8abfd019f328eeb22d2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35efab986d7faeda540f744d92e1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
A.4 | B.8 | C.![]() | D.![]() |
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内蒙古乌兰察布市四子王旗宽高实验学校2023-2024学年高二上学期期中数学试题(已下线)江苏省南通市如皋市2023-2024学年高二上学期教学质量调研(一)数学试题河南省三门峡市渑池县第二高级中学2023-2024学年高二上学期第二次月考(11月)数学试题(已下线)2.3.1 两条直线的交点坐标、两点间的距离公式【第二课】福建省漳州市东山县2023-2024学年高二上学期期中数学试题黑龙江省哈尔滨市第九中学校2023-2024学年高二上学期12月月考数学试题(已下线)期末考试押题卷三(考试范围:苏教版2019选择性必修第一册)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
5 . 如图,已知四棱锥
中,
平面
,四边形
中,
,
,
,
,
,点
在平面
内的投影恰好是
的重心
.
(1)求证:平面
平面
;
(2)求线段
的长及直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/27/d1cdac40-7172-48c9-8a19-7133bb086f67.png?resizew=147)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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6 . 直线
,若直线分别与x轴,y轴的负半轴交于A、B两点,求三角形AOB面积的最小时的直线的方程______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cadd4cfce20dc27aa13c67afe46d2ddc.png)
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内蒙古乌兰察布市四子王旗宽高实验学校2023-2024学年高二上学期期中数学试题河北省河北师范大学附属中学2023-2024学年高二上学期10月月考数学试题(已下线)高二数学上学期期中模拟卷01(原卷版)
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解题方法
7 . 向量
,
,在直线l方向向量上的投影向量相等,则直线l的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f4dcf415977dea53f52a85b6b82136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc77f4da163cb8800d6a92637912077e.png)
A.1 | B.-1 | C.2 | D.-2 |
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解题方法
8 . 设直线
的方程为
.
(1)求证:不论
为何值,直线
必过一定点
;
(2)若直线
分别与
轴正半轴,
轴正半轴交于点
,
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8fe35cf3dbbef99a946fd1acc30fd1.png)
(1)求证:不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若直线
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f4e48c2b39a2d944c3b8cff204f70e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b711c6b3cad2fa767b9f63f403d75751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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9 . 如图,在棱长为2的正方体
中,棱
的中点为
,则平面
截正方体的外接球所得截面圆的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/190ccdc4-d6e3-4c07-8c20-7ad6f17907b7.png?resizew=150)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 如图,二面角
等于
,
、
是棱
上两点,
、
分别在半平面
、
内,
,
,且
,
,
,则
的长等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71e6ea7333dbc78d0a7b9bc3892f940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/ddd03c85-0f90-43df-af86-e2962f59b374.png?resizew=170)
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