1 . 如图,数轴
,
的交点为
,夹角为
,与
轴、
轴正向同向的单位向量分别是
,
.由平面向量基本定理,对于平面内的任一向量
,存在唯一的有序实数对
,使得
,我们把
叫做点
在斜坐标系
中的坐标(以下各点的坐标都指在斜坐标系
中的坐标).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/47c86fcb-b324-44cd-898f-5ee38bd1144a.png?resizew=106)
(1)若
,
为单位向量,且
与
的夹角为
,求点
的坐标;
(2)若
,点
的坐标为
,求向量
与
的夹角;
(3)若
,求过点
的直线
的方程,使得原点
到直线
的距离最大.
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adda40c31079000eb6fbb188e9ea28d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b257fe21a91d22e853b1642c9d44647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adda40c31079000eb6fbb188e9ea28d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/47c86fcb-b324-44cd-898f-5ee38bd1144a.png?resizew=106)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b12fe9a4054ffbacca1b995751969a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42206793edde00d2d43cd07adf78366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b054aac706341436cb337b6561dd0aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72bf0fce80daad394f2a9d013829c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82df2769a0779574c65cd4eae7be4ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-03-05更新
|
678次组卷
|
3卷引用:专题4.1 坐标平面上的直线【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)
(已下线)专题4.1 坐标平面上的直线【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市复旦大学附属中学2015-2016学年高二上学期期中数学试题苏教版(2019) 选修第一册 一蹴而就 第1章 单元测试
名校
2 . 在
中,已知
、
.
(1)若点
的坐标为
,直线
,直线
交
边于
,交
边于
,且
与
的面积之比为
,求直线
的方程;
(2)若
是一个动点,且
的面积为
,试求
关于
的函数关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f89b18f69812fb34fd1290e2f1b36aa.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c293fdb849822d49c621971e47f6627f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29f3123f57b56444be9bc048eacc82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4b17ce6e90cd3810a3696262e94c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9a016fd7021b9e9625c8d5f0938ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2019-12-10更新
|
463次组卷
|
4卷引用:专题3.1 坐标平面上的直线【易错题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)
(已下线)专题3.1 坐标平面上的直线【易错题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市金山中学2019-2020学年高二上学期期中数学试题上海市位育中学2018-2019学年高二上学期10月月考数学试题上海市位育中学2020-2021学年高二上学期10月月考数学试题
名校
3 . 圆
的圆心到直线
的距离等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38498095f8db1e2e4f3b430629fd095f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a6b676fc870f63c2431b66de9762af.png)
您最近一年使用:0次
2019-11-10更新
|
580次组卷
|
5卷引用:专题2.1 坐标平面上的直线【章节复习专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)
(已下线)专题2.1 坐标平面上的直线【章节复习专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市致远高级中学2020-2021学年高二上学期期末数学试题上海市进才中学2018-2019学年高二上学期期末数学试题上海市川沙中学2019-2020学年高一上学期期末数学试题上海海洋大学附属大团高级中学2023届高三上学期一模数学试题
名校
4 . 已知直线
过点
,且它的一个方向向量为
,则原点
到直线
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c76c41773aae617db1c0cc04bcf836f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
5 . 若复数
复平面上对应的点在直线
上,则
的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6d334cdda2dffb482842af63581e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29c54b5d80496acc51aaa9e0123e0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
您最近一年使用:0次