2.2.2平面向量的数乘运算.pdf

人人参与课堂人人体验成功第1页有效教学高效学习行动路线图之必修4-第二章平面向量课题：2.2.2 平面向量的数乘运算班级：组名：姓名：问题导读评价单探究一向量的数乘运算的概念：实数 与向量 a 的积是一个，这种运算叫做，记作 a，其长度与方向规定如下：|a|.a(a0)的方向当时，与 a方向相同当时，与 a方向相反；特别地，当 0 或 a0 时，0a或0 .探究二向量数乘的运算律(a)；()a；(ab).探究三向量的线性运算(1)向量的加、减、数乘运算统称为向量的线性运算对于任意向量a，b，以及任意实数、m、n，恒有(manb).(2)向量 a(a0)与 b 共线，当且仅当有唯一一个实数，使.问题解决评价单例一 已知 a，b 是两个非零向量，判断下列各命题的对错，并说明理由(1)2 a 的方向与 a 的方向相同，且2a的模是 a 的模的 2 倍；(2)2a 的方向与 5a 的方向相反，且 2a的模是 5a 的模的25；(3)2a 与 2a 是一对相反向量；(4)ab 与(ba)是一对相反向量；(5)若 a，b 不共线，则 a 与 b 不共线例二 (1)已知 3(xa)3(x2a)4(xab)0(其中 a，b 为已知向量)，求 x；人人参与课堂人人体验成功第2页(2)已知3x4ya，2x3yb，其中 a，b为已知向量，求x，y.例三 已知 e1，e2是共线向量，a3e14e2，b6e18e2，则 a 与 b 是否共线？例四 平行四边形 ABCD 中，ADuu u rb，ABuuu ra，M为 AB中点，N为 BD靠近 B的三等分点，求证：M、N、C三点共线问题拓展评价单一、选择题1已知 M是 ABC的 BC边上的中点，若向量ABuuu ra，ACuuu rb，则向量AMuuuu r等于()A.12(ab)B.12(ba)C.12(ab)D12(ab)2将1122(2 a8b)4(4a2b)化成最简式为()文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5人人参与课堂人人体验成功第3页A2abB2ba C ab Dba3设 a 与 b 是两个不共线的向量，且向量ab 与(b2a)共线，则实数 的值等于()A12B.12 C 2 D2 4(2010湖北高考)已知ABC和点M满足MAuuurMBuuurMCuuu u r0.若存在实数m使得ABuuu rACuuu rmAMuuuu r成立，则 m()A2 B3 C4 D5 二、填空题5若xya；2x3yb.则 x_，y_.6下列两个命题：对于实数 m和向量 a、b，恒有 m(ab)ma mb；对于实数 m、n 和向量 a，恒有(m n)ama na.其中正确命题的序号为 _三、解答题7已知非零向量e1、e2不共线，且ABuuu re1e2，BC ke18e2，CDuuu r3(e1e2)，若 A、B、D三点共线，试确定实数k 的值8.如图，已知平行四边形ABCD 的边 BC、CD上的中点分别为K、L，且AKuuu re1，ALuuu re2，试用 e1，e2表示BCuuu r，CDuuu r.文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 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ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5人人参与课堂人人体验成功第4页【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、纪律情况向量的数乘运算及几何意义参考答案问题导读评价单探究一向量 向量的数乘|a|0 0，2a 与 a 同向，且|2a|2|a|.(2)正确 50，5a 与 a 同向，且|5 a|5|a|.20，2a 与 a 反向，且|2a|2|a|.(3)正确(4)错误(ba)baab.(5)错误 0a0，0 与任一向量共线例二(1)原方程化为 3x3a3x6a4x4a4b0.得 2xa4b0，即 2x4ba.x2b12a.(2)3x4ya，2x3yb，由得 y23x13b，代入，得 3x423x13ba，3x83x43ba,17x4b3a，x317a417b.y23317a417b 13b217a851b13b217a317b.综上可得x317a417b，y217a317b.文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5人人参与课堂人人体验成功第6页例三 e1，e2共线，存在 R，使 e1e2.a3e14e23e24e2(3 4)e2，b6e18e26e28e2(68)e2，a3468b(43)，a 与 b 共线，43，b0 时，a 与 b 也共线例四 在ABD中，BDuuu rADuuu rABuuu r，ABuuu ra，ADuuu rb，BDuuu rba.N点是 BD的三等分点，BNuuur13BDuu u r13(ba)BCuuu rb，CNuuu rBNuuu rBCuuu r13(ba)b13a23b.M为 AB中点，MBu u ur12a，CMu u urMCu u u r(MBu u urBCu u u r)12ab 12ab.由可得：CMu u ur32CNu u ur.由共线向量定理知：CMu u urCNu u u r，又CMu u ur与CNuuu r有公共点 C，C、M、N三点共线问题拓展评价单1 解析：根据平行四边形法则知ABuuu rACuuu r2AMuuuu r，文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5人人参与课堂人人体验成功第7页AMuuuu r12(ABuuu rACuuu r)12(ab)答案：C 2 解析：原式112(4 a16b16a8b)112(12a24b)2ba.答案：B 3 解析：(b2a)2ab.ab 与 2ab 共线，121?12.答案：A 4 解析：由MAuuu rMBuuurMCuuu u r0 得点 M是 ABC 的重心，可知AMuuuu r13(ABuuu rACuuu r)，ABuuu rACuuu r3AMuuuu r，则 m 3.答案：B 5 解析：由 xya 可得 yax，把此式代入 2x3yb 得，2x3(ax)b，解得 x3ab，yaxb2a.答案：3abb2a6 解析：满足实数与向量积的运算律答案：7 解：BDuuu rBCuuu rCDuuu rke18e23(e1e2)(k3)e15e2.A、B、D三点共线，存在实数，使ABuuu rBDuuu r，即 e1e2(k3)e15e2 整理得 e1e2(k3)e15e2，即(k3)1 e1(15)e2，又 e1、e2不共线，k310，150，则k2，15.k2.8 解：法一：设BCuuu rx，则BKuuu r12x，ABuuu re112x，DLuuu r12e114x，又ADuuu rx，由ADuuu rDLuuu rALuuu r得：文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5人人参与课堂人人体验成功第8页x12e114xe2，解方程，得 x43e223e1，即BCuuu r43e223e1，由CDuuu rABuuu r，ABuuu re112x，得：CDuuu r43e123e2.法二：设BCuuu rx，CDuuu ry，则BKuuu r12x，DLuuu r12y.由ABuuu rBKuuu rAKuuu r，ADuuu rDLuuu rALuuu r得：y12xe1，x12ye2，2得12x2xe12e2，解得：x23(2 e2e1)，即BCuuu r23(2e2e1)43e223e1，同法得 y23(2e1e2)，即CDuuu r43e123e2.文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5文档编码:CY4Z3S1L9Z1 HH1S4P2D8B3 ZE3K2H1O5V5