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1、第1页1213课题：2.4.2 平面向量数量积的坐标表示、模、夹角问题导读评价单探究一.两向量的数量积与两向量垂直的坐标表示。已知两个非零向量1122a=xy,b=xy,a b=vvv v（坐标形式）。这就是说：（文字语言）两个向量的数量积等于。设1122a=x,y,b=x,y,vv则abvv_ 探究二.三个重要公式平面内两点间的距离公式：设a=(x,y),v则2a=v_ 或av_。平面内两点间的距离公式：若1122x,y,B=x,yA,则ABuuu r_ 两向量夹角公式：（0）cos _ _ 自主练习1.a=2 b=2a,brrr r且夹角为 450,使b-aar rr与垂直，则_ 2.a=
2、(1,2),b=(x,1)a+2b2abx=rrruu rrr且与平行，则_ A.2 B.1 C.D.3.a=(1,2)b=(1,)abmrrrr若 与的夹角为锐角，则m的取值范围为 _ 4.设1122a=(x,y),b=(x,y)rr有以下命题：2211a=x+y;r2222b=x+y;r1212a b=x x+y y;r rg1212abx x+y y=0rr。其中假命题的序号是_.问题解决评价单题型一数量积的坐标运算第2页例1.已知向量ar=（1,3），br=（2,5），cr=（2,1）求a brr；()(2)ababrrrr；a bcr rr，ab crr r例2.已知向量abrr与同
3、向，br=（1,2），a br r=10，求向量ar的坐标；若cr=（2,1），求b car rr及a bcr rr。题型二。两向量的夹角问题例3.已知ABCV定点的坐标分别为A(3,4),B(0,0),C(c,o),若c=5，求sin A的值；若A是钝角，求c的取值范围。例 4已知(1,1)ar，(,1)br，若abrr与的夹角为钝角，求的取值范围。题型三.向量垂直的坐标表示文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P
4、10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S
5、1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:C
6、M5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3
7、B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK
8、7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8
9、L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1
10、HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3第3页例 5.已知13(,)22ar，OAabu uu rrr，OBabu uu rrr,若AOBV是以 O 为直角顶点的等腰直角三角形，求向量br。例 6.已知(1,2)ar，(2,3)br，若
11、向量cr满足carrbr，cabrrr，求向量cr的坐标。问题拓展评价单1在四边形ABCD 中，若ABuuu rCDuuu r0r，ACuuu r?BDuuu r0，则四边形为()A平行四边形B矩形C等腰梯形D菱形2已知两个力F1，F2 的夹角为90，它们的合力大小为10 N，合力与 F1 的夹角为60，那么 F1 的大小为()A53 N B5 N C10 N D52 N 3设向量ar(1，3)，br(2,4)若表示向量4ar、3br2ar、cr的有向线段首尾相接能构成三角形，则向量cr为()A(1，1)B(1,1)C(4,6)D(4，6)4O 为平面上的定点，A,B,C 是平面上不共线的三点
12、，若(OBuuu rOCuuu r)?(OBuuu rOCuuu r2OAuuu r)0，则 ABC 是()A以 AB 为底边的等腰三角形B以 BC 为底边的等腰三角形C以 AB 为斜边的直角三角形D以 BC 为斜边的直角三角形5若 A(1,2)，B(2,3)，C(2,5)，则 ABC 的形状为 _文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1
13、HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3
14、J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档
15、编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y
16、10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O
17、6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P
18、10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S
19、1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3第4页6.已知ABuu u r(6,1)，BCuuu r(x，y)，CDuuu r(2，3)若BCuuu rDAu uu r，ACBDu uu ruu u r，(1)求 x，y 的值；(2)求四边形ABCD 的面积7两个力F1irjr，F24ir5jr作用于同一质点，使该质点
20、从A(20,15)移动到点B(7,0)(其中ir、jr分别是 x 轴、y 轴正方向上的单位向量)求：(1)F1，F2分别对该质点做的功；(2)F1，F2的合力 F 对该质点做的功【未解决问题】自我评价同伴评价学科长评价小组长评价学术助理评价1、完成单子情况2、主动帮助同伴3、主动展讲4、主动补充与质疑5、纪律情况2.4.2 自主练习文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文
21、档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6
22、Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10
23、O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5
24、P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10
25、S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:
26、CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N
27、3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3第5页1.=2 2.C 3.12m且m 2 4.例 1（1）17（2）8（3）34,17,(9,27)例 2 （1）（2,4）（2）0r，（20，-10）例 3（1）2 55（2）253c例 4 1-1或 1例 5 3 131(,)2222或
28、（-，-）例 67793（-，-）巩固训练1D.2.B 3.D 4.B 5.直角三角形6.解：(1)ADuuu rABuuu rBCuuu rCDuuu r(4x，y 2)，DAuuu r(4x,2y)由BCuuu rDAuuu r，得 x(2y)y(4x)0.ACuuu rABBCuuu ru uu r(6x，y1)，BDBCCDuuu ru uu ruuu r(x 2，y3)由ACuuu rBDuuu r，得(6x)(x 2)(y 1)(y 3)0.由，解得x2，y 1 或 x 6，y3.(2)S四边形ABCD 12|ACuuu r|BDuuu r|，当 x 2，y 1 时，S四边形ABC
29、D16；当 x 6，y3 时，S四边形ABCD16.即四边形ABCD 的面积为16.7.解：ABuuu r(720)ir(015)jr 13ir15jr.(1)F1做的功 W1F1?sF1?AB (irjr)?(13ir15jr)28 J.F2做的功 W2 F2?sF2?AB (4ir5jr)?(13ir15jr)23 J.(2)FF1F2 5ir4jr.所以 F 做的功 WF?sF?AB(5ir4 jr)?(13ir 15jr)5 J.文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7
30、X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L
31、10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 H
32、Q5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J
33、10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编
34、码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y1
35、0N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3文档编码:CM5V3J10S1L1 HQ5P10C8L10O6 ZK7X6Y10N3B3