2024高二上·全国·专题练习
1 . 如图,已知某市穿城公路
自西向东到达市中心O后转向正北方向,
,现准备修建一条直线型高架公路L,在
上设一出入口A,在
上设一出入口B. 且要求市中心O到
所在直线的距离为10 km.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ed3911d2-ae66-4371-98f3-f2c7c0489c52.png?resizew=142)
(1)若将出入口A设计在距离中心O点
km处,求A,B两出入口间的距离;
(2)在公路
段上距离市中心O点30 km处有一古建筑C(视为点),现设立一个以C为圆心,5 km为半径的圆形保护区(包含边界),问如何在古建筑C和市中心O之间设出入口A,才能使高架公路及其延长线不经过保护区?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1eb76f88cb973c220cffa1c9c0721a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28986ee88e684ebb6020d5f69047ccb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ed3911d2-ae66-4371-98f3-f2c7c0489c52.png?resizew=142)
(1)若将出入口A设计在距离中心O点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fdaf9c9ae3eb3d4077ea8aa38dd90.png)
(2)在公路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
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2 . 在解析几何中,设
,
为直线
上的两个不同的点,则我们把
及与它平行的非零向量都称为直线
的方向向量,把与直线
垂直的向量称为直线
的法向量,常用
表示,此时
.若点
,则可以把
在法向量
上的投影向量的模叫做点
到直线
的距离.现已知平面直角坐标系中,
,
,
,则点
到直线
的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4e5fd273fac49c02beab39164a4fd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0b2e465d7953afb39c4099bafbdd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331998dcf1d3c18776c94fb2077cd7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891fd9ff3c8a478691f3f8ef2213c80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ff297bc1b729cc99dbf3cfaabc4a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f05b989842734d1afd9429d15f5484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630ae392041c579e8a895bdf3ad37ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-29更新
|
180次组卷
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2卷引用:浙江省杭州第二中学2023-2024学年高一上学期期末数学试题
解题方法
3 .
为直角梯形,
,
,
,
平面
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/ed58de43-d6f3-4f23-b0fa-75daf3b72b4f.png?resizew=166)
(1)求证:
;
(2)求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b5ea5627440c19999a9039eaa1c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d150134e5018f74fc4e8a016ced5f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e7191b68d9f70d08bc40dd774b390d.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/00803e67a5d417a9a4dc00277fca778b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/ed58de43-d6f3-4f23-b0fa-75daf3b72b4f.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c231fb9aeaf4b73c2d835bb4c3d42b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
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解题方法
4 . 已知点
,
,且平行四边形
的四个顶点都在函数
的图像上,则平行四边形
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6d861cf80bd971be02918cfa58cb76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6ea89ac89df0bb030859d178c3595a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac56c56432bda6201a06c602234d1901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
5 . 已知
顶点
,边
上的高
所在直线方程为
,边
上的中线
所在的直线方程为
.
(1)求直线
的方程:
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c53c2ce5532642de107e0d85c75f3e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a362b22d77130726c8dda391382eb186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4771786f8a08f8e0bf7ce17d73fcfb9a.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-12-23更新
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264次组卷
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3卷引用:广东省茂名市高州中学2023-2024学年高一下学期期中考试数学试题(创新班1-3班)
6 . 已知直线
:
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67158a9694092c5c9a781be29953f96.png)
A.直线![]() ![]() |
B.若直线![]() ![]() |
C.点![]() ![]() |
D.过![]() ![]() ![]() |
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2023-12-11更新
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596次组卷
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4卷引用:河北省保定市部分学校2023-2024学年高一下学期1+3期中考试数学试题
7 . 已知实数
、
、
、
满足:
,
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de38bc7405c8e0cf130ba2d13c374783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4017e4ab7a3ebbc318ec0072e855f4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a7dbebaf2840e6be93bc475b0e8002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a945df01631dfc920d259e35ea5fc385.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-20更新
|
226次组卷
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2卷引用:江西省宜春市丰城市第九中学2023-2024学年高一上学期期末数学试题
8 . 如图,已知长方体ABCD-A1B1C1D1中,AB=2,AA1=AD=1,求:
(2)点D1到直线AC的距离.
(3)直线AB与面A1DCB1的距离.
(2)点D1到直线AC的距离.
(3)直线AB与面A1DCB1的距离.
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