2022年平面向量的坐标表示 .pdf

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1、学习好资料欢迎下载课题名称：平面向量的坐标表示教材版本：江苏省职业学校文化课教材基础模块年级：高一撰写教师：王康康一、教材分析教学内容“平面向量的坐标表示（一）”位于江苏省职业学校文化课教材基础模块，下册第七章第三节，该节内容分两课时，本节课是第一课时：以火箭升空的速度分解为水平向前和竖直向上的两个分速度，来探究平面向量的坐标形式，引出平面向量的坐标表示。教材的地位和作用本节课内容巩固了前二节的知识，利用向量加法及数乘来研究新知，也为下一节课“向量的直角坐标运算”及今后的学习空间向量和立体几何打下基础。教学重点、难点教学重点:会写出给定向量的坐标（解决办法：通过物理学中速度的分解帮助学生认识平

2、面向量的坐标形式，通过例题讲解让学生掌握向量的坐标表示。）教学难点:理解平面向量的坐标表示（解决办法：从实际物理量“速度”的分解引入，利用向量加法的平行四边形法则对坐标系内向量进行分解，赋予向量坐标几何意义。）二、教学目标分析知识与技能：识记平面向量的直角坐标的含义，能根据定义求所给向量的直角坐标，会通过平面向量的直角坐标求模。过程与方法：通过探究向量加法的平行四边形法则的过程，进一步培养学生的归纳猜想类比运用数学知识解决实际问题等能力，和探究性学习的能力。情感、态度、价值观：结合实际问题，激发学生学习数学的兴趣，通过小组讨论的形式来培养学生的合作交流的学习方式及自主学习的态度。二、学情分析班

3、级现状我带的是 11 级计算机专业综合高中2、4 班，学生的数学基础相对较差，好在这两班的学生大多数学生对数学学习尚有一定兴趣，上课也很积极，与教师沟通较好，故此教师应因势利导，引导学生积极参与探究，指导学生合作互动，讨论交流。知识现状学生已经学习了向量加法及数乘，对分解的向量，及用某个方向上的单位向量表示该方向的向量有了初步的认识，为本节课的学习提供了方法和思想。预测困难经过前两节的学习，学生对相等向量已经了解，对学生但对向量可以平移并且坐标不变，学习起来可能有一定的难度。另外综高学生在抽象思维概括能力、数形结合能力等方面还有待加强三、选择媒体资源学习好资料欢迎下载媒体资源 1 名称：火箭升

4、空视频媒体格式：WMA媒体资源 2 名称：课件媒体格式：ppt 媒体资源 3名称：实物投影仪四、教学活动教学活动一览表教学活动 1：创设问题情境5mins教学活动 2：探究平面向量的坐标表示10mins教学活动 3：应用举例、加深理解12mins教学活动 4：随堂练习，反馈评价15mins教学活动 5：课堂小结2mins 教学活动 6：作业布置 1mins各个教学活动框架教学活动 1：创设问题情境5mins书 50 页探究文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:

5、CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 H

6、G1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 Z

7、T2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编

8、码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3

9、 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9

10、 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文

11、档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6学习好资料欢迎下载教师活动：教师播放火箭升空的视频，让学生感受实际生活的问题，然后出示ppt 把火箭速度分解为水平和竖直两个方向上分速度，让学生回答以上三个问题，学生活动：让学生思考回答以上三个问题，教师在扩展两个向量让学生回答。IP 资源：视频、图片，ppt 教学活动 2：探究平面向量的坐标表示10minsM N O 2eaP a(,)P x yO ijM N 1212(1),;(2),;(3),eeOMONOMONOPeeOP分别

12、用单位向量表示用表示用单位向量表示。OPOMONOPxiy j即axiy j平面直角坐标系中任一向量都可以唯一地表示成的形式文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2

13、X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:

14、CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 H

15、G1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 Z

16、T2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编

17、码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3

18、 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6学习好资料欢迎下载得到向量的坐标表示概念：教师活动：教师把火箭速度分解问题，抽象到直角坐标系中，在让学生思考平面直角坐标系中任意向量怎么分解

19、到x 轴和 y 轴上，引出向量的坐标形式，得到向量的坐标表示学生活动：让学生思考平面上任意向量的分解，学生自主思考的到新知IP 资源：图片，ppt 教学活动 3：应用举例、加深理解12mins例 2.如图所示，写出向量的坐标，并求出模.教师活动：引导学生思考，教师出示完整的解题过程学生活动：学生思考，齐声回答IP 资源：ppt 教学活动 4：随堂练习，反馈评价15mins教师活动：让学生在学案上做练习，教室巡视到学生中来观察学生解题情况，进行指导。然后把学生的解题用实物投影仪，投给学生看，找学生评价，教师点评IP 资源：实物投影仪五、备课后记通过播放视频激发学生的学习兴趣，在通过 ppt 播放

20、图形，让学生能直观感受平面向量的坐标表示的形式，利用课件也能节省时间，增加教学容量，通过实物投影学生的练习，让学生互评，时反馈学生学习情况，及时进行评价。如果用这份教案上课，我需要做个学案，上面有相应的图形，方便学生练习画图及教师投影；在日常教学中可以用这种方法备课和上课，但是教师的工作量会很大。y O x abcdeaxiy ja叫做的坐标形式(,)ax ya叫做 的坐标表示22axy1.143(2)3aijbicj例 写出下列坐标的坐标表示,并以 O为起点作出下列各个向量（3）,a b c d文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4

21、X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M

22、10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X

23、8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:C

24、D4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG

25、1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT

26、2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码

27、:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6学习好资料欢迎下载文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4

28、X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M

29、10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X

30、8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:C

31、D4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG

32、1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6文档编码:CD4X8P5R6C3 HG1M10Y7Z5L9 ZT2X8D4K4J6