2022年人教A版高中数学必修四2.4《平面向量的数量积》导学案2 .pdf

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1、名师精编优秀教案高中数学人教版必修4：2.4 平面向量的数量积导学案【学习目标】1、知道平面向量数量积的含义及其物理意义；2知道平面向量数量积积与投影的关系；3、会运用平面向量的数量积及其运算律.【重点难点】重点：向量数量积的定义及运算律难点：数量积的应用【知识链接】1、向量的线性运算；2、向量),(11yxa，),(22yxb共线01221yxyx.【学习过程】阅读课本第103 页到第 105 页的内容，尝试回答以下问题：知识点 1:平面向量数量积的物理背景及其含义问题 1物体在 力 F 作用下产生位移S，那么力F 所做的功_W.力和位移是矢量，功是 标量，类比我们引入两个向量的数量积的概念

2、：已知两个非零向量a与b，我们把 _叫做a与b的数量积,记作ab，即 _ _,其中是a与b的夹角.问题 2、请叙述投影的定义.问题 3、由投影的定义，你能叙述ba的几何意义吗？问题 4设a与b是非零向量则：（1）_ba；（2）当a与b同向时，ba=_；当a与b反向时，ba=_.特别地aa=_,a=_;名师精编优秀教案（3）baba_；（4）babacos.问题 6、尝试用数量积的运算律证明下列等式：（1）2222abaa bb；（2）22ababab；例 1、已知5a，2b，a与b的夹角为120，求23abab的值.知识点 2:平面向量数量积的坐标表示，模，夹角阅读课本第106 页到 107

3、页的内容，尝试回答以下问题：问题 1、已知两个非零向量),(11yxa，),(22yxb，怎样用a与b的坐标表示ba呢？（提示：jyixa11，jyixb22）问题 2由问题1，若),(yxa，则2a=_，或a=_.问题 3、如果),(11yxa，),(22yxb，是a与b的夹角，则_cos.例 2、在ABC中，已知)2,1(A，)1,3(B，)2,5(C，求BACACABcos,.文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q

4、2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV

5、2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q

6、2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV

7、2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q

8、2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV

9、2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q

10、2 ZZ7R7S1Q2Y2名师精编优秀教案【基础达标】A1、已知8,6,pqp和q的夹角是60，求p q.A2已知6a，e为单位向量，当a与e之间夹角分别为135,90,45时，分别求出a在e方向上的投影.B3、已知）（3,2a，）（4,2b，）（2,1c，求ba，）（）（baba，)(cba，2)(ba.B4、已知4a，3b，61)2)(32(baba，求ba的夹角.C5、在ABC中，设bCAaBCcAB,，且accbba，试判断ABC的形状.文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S

11、1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y

12、9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S

13、1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y

14、9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S

15、1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y

16、9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S

17、1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2名师精编优秀教案D6、已知ba是两个非零向量，且满足baba，求a与ba的夹角【小结】【当堂检测】A1、已知ABC中，5,8,60BCACC,求BCCA.B2、求证：A(1，0)，B(5，-2),C(8,4),D(4,6)为顶点的四边形是一个矩形.【课后反思】本节课我最大的收获是我还存在的疑惑是我对导学案的建议是文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 H

18、L2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2

19、Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 H

20、L2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2

21、Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 H

22、L2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2

23、Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 H

24、L2Z7V7S1Q2 ZZ7R7S1Q2Y2名师精编优秀教案文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 Z

25、Z7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9

26、Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 Z

27、Z7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9

28、Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 Z

29、Z7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2