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1、第1页第二章平面向量课题：2.5 平面向量应用举例问题导读评价单1、平行四边形是表示向量加法和减法的几何模型,如图,你能观察、发现并猜想出平行四边形对角线的长度与两邻边长度之间有什么关系吗？你能利用所学知识证明你的猜想吗？能利用所学的向量方法证明吗？试一试可用哪些方法?你能总结一下利用平面向量解决平面几何问题的基本思路吗？2、在日常生活中，你是否有这样的经验：两个人共提一个旅行包，夹角越大越费力；在单杠上作引体向上运动，两臂的夹角越小越省力你能从数学的角度解释这种现象吗？1、用向量方法解决平面几何问题的“三步曲”：(1)建立平面几何与向量的联系,用_ 表示问题中涉及的几何元素,将平面几何问题转
2、化为 _;(2)通过_,研究几何元素之间的关系,如距离、夹角等问题;(3)把运算结果“翻译”成几何关系.2、向量在物理中的应用1.力、速度、加速度、位移都是向量.2.力、速度、加速度、位移的合成与分解运用的就是向量的加减法，其运算法则就是平行四边形法则和三角形法则.3.动量 mv 就是数学上的数与向量的乘法运算.4.功即是力 F与所产生位移 s 的数量积.问题解决评价单例 1 如图,ABCD 中,点 E、F 分别是 AD、DC 边的中第2页点,BE、BF 分别与 AC 交于 R、T 两点,你能发现 AR、RT、TC 之间的关系吗?例 2 如图,AD、BE、CF 是ABC 的三条高.求证:AD、
3、BE、CF 相交于一点.例 3 如图,在 RtABC 中,已知 BC=a.若长为 2a的线段 PQ 以点 A 为中点,问:BCPQ与的夹角 取何值时,CQBP?的值最大?并求出这个最大值.例 4 在水流速度为 43 km/h 的河水中，一艘船以12 km/h 的实际航行速度垂直于对岸行驶，求这艘船的航行速度的大小与方向问题拓展评价单1一物体受到相互垂直的两个力f1、f2的作用，两力大小都为53N，则两个力的文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V
4、9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L1
5、0J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6
6、Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P
7、4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8
8、L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5
9、G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N
10、4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1文档编码:CE4N4P4V9N2 HB6Z4X8L10J5 ZL5W2K5G6Q1第3页合力的大小为()A103N B0N C56N D.562N 2河水的流速为2m/s，一艘小船想以垂直于河岸方向10m/s 的速度驶向对岸，则小船在静水中的速度大小为()A10m/s B226m/s C4 6m/s D12m/s 3已知向量 a(x1，y1)，b(x2，y2)，若|a|2，|b|3，ab6，则x1y1x2y2的值为()A.23B23 C.56D564已知一物体在共点力F1(lg2，lg2)，F2(lg5，lg2)的作用下产生位移S
11、(2lg5,1)，则共点力对物体做的功W为()Alg2 Blg5 C1 D2 5在 ABC所在的平面内有一点P，满足 PAPBPCAB，则 PBC与ABC的面积之比是()A.13 B.12 C.23D.346 已知向量 a，e 满足：ae，|e|1，对任意 t R，恒有|at e|ae|，则()AaeBa(ae)Ce(ae)D(ae)(ae)7已知|OA|1，|OB|3，OAOB，点 C在AOB 内，AOC 30，设 OCmOAnOB，则mn()A.13 B3 C33 D.3 328在平面直角坐标系xOy中，已知点 A(1，2)，B(2,3)，C(2，1)(1)求以线段 AB、AC为邻边的平行
12、四边形的两条对角线的长；文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
13、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
14、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
15、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
16、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
17、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
18、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3第4页(2)设实数 t 满足(ABtOC)OC0，求 t 的值9一条宽为3km的河，水流速度为2km/h，在河两岸有两个码头A、B，已知 AB3km，船在水中最大航速为4km/h，问该船从 A码头到 B码头怎样安排航行速度可使它最快到达彼岸B码头？用时多少？【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
19、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2.5 平面向量应用举例参考答案文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U
20、7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I
21、4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U
22、7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I
23、4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U
24、7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I
25、4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3第5页【研讨互动，问题生成】图 2 证明:方法一:如图 2.作 CEAB 于 E,DFAB 于 F,则 RtADF RtBCE.AD=BC,AF=BE.由于 AC AE2+CE2=(AB+BE)2+CE2=AB2+2AB BE+BE2+CE2=AB2+2AB BE+BC
26、2.BD2=BF2+DF2=(AB-AF)2+DF2=AB2-2AB AF+AF2+DF2=AB2-2AB AF+AD2=AB2-2AB BE+BC2.AC2+BD2=2(AB2+BC2).图 3 方法二:如图 3.以 AB 所在直线为x 轴,A 为坐标原点建立直角坐标系.设 B(a,0),D(b,c),则 C(a+b,c).|AC|2=(a+b)2+c2=a2+2ab+b2+c2,|BD|2=(a-b)2+(-c)2=a2-2ab+b2+c2.|AC|2+|BD|2=2a2+2(b2+c2)=2(|AB|2+|AD|2).用向量方法推导了平行四边形的两条对角线与两条邻边之间的关系.在用向量方
27、法解决涉及长度、夹角的问题时,常常考虑用向量的数量积.通过以下推导学生可以发现,由于向量能够运算,因此它在解决某些几何问题时具有优越性,它把一个思辨过程变成了一个算法过程,学生可按一定的程序进行运算操作,从而降低了思考问题的难度,同时也为计算机技术的运用提供了方便.教学时应引导学生体会向量带来的优越性.因为平行四边形对角线平行且相等,考虑到向量关系DB=AB-AD,AC=AB+AD,教师可点拨学生设AB=a,AD=b,其他线段对应向量用它们表示,涉及长度问题常常考虑向量的数量积,为此,我们计算|AC|2与|DB|2.因此有了方法三.方法三:设AB=a,AD=b,则AC=a+b,DB=a-b,|
28、AB|2=|a|2,|AD|2=|b|2.|AC|2=ACAC=(a+b)(a+b)=a a+a b+b a+b b=|a|2+2a b+|b|2.同理|DB|2=|a|2-2a b+|b|2.观察两式的特点,我们发现,+得|AC|2+|DB|2=2(|a|2+|b|2)=2(|AB|2+|AD|2),文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
29、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
30、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
31、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
32、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1
33、 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3
34、B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3第6页即平行四边形两条对角线的平方和等于两条邻边平方和的
35、两倍.【合作探究，问题解决】例 1 解:如图 4,设AB=a,AD=b,AR=r,AT=t,则AC=a+b.由于AR与AC共线,所以我们设r=n(a+b),nR.，又因为EB=AB-AE=a-21b,又ER与EB共线,所以我们设ER=mEB=m(a-21b).因为ERAEAR,所以 r=21b+m(a-21b).因此 n(a+b)=21b+m(a-b),即(n-m)a+(n+21m)b=0.由于向量a、b 不共线,要使上式为0,必须.021,0mnmn解得 n=m=31.所以AR=31AC,同理TC=31AC.于是RT=31AC.所以 AR=RT=TC.例 2 证明:设 BE、CF 相交于 H
36、,并设AB=b,AC=c,AH=h,则BH=h-b,CH=h-c,BC=c-b.因为BHAC,CHAB,所以(h-b)c=0,(h-c)b=0,即(h-b)c=(h-c)b.化简得 h(c-b)=0.所以AHBC.所以 AH 与 AD 共线,即 AD、BE、CF 相交于一点H.例 3 解:方法一,如图 7.ABAC,ABAC=0.ACAQCQABAPBPAQAP,)()(ACAQABAPCQBP?=ACABAQABACAPAQAP?=-a2-AP AC+ABAP=-a2+AP(AB-AC)文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S
37、3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E
38、1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S
39、3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E
40、1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S
41、3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E
42、1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S
43、3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3第7页=-a2+21PQBC=-a2+a2cos.故当 cos=1,即=0,PQ与BC的方向相同时,CQBP?最大,其最大值为0.方法二:.以直角顶点A 为坐标原点,两直角边所在的直线为坐标轴,建立如图所示的平面直角坐标系.设|AB|=c,|AC|=b,则 A(0,0),B(c,0),C(0,b),且|PQ|=2a,|BC|=a.设点 P 的坐标为(x,y),则 Q(-x,-y).BP=(x-c,y),CQ=(-x,-y-b),BC=(-c,b),PQ=(-2x
44、,-2y).CQBP?=(x-c)(-x)+y(-y-b)=-(x2+y2)+cx-by.cos=2|abycxBCPQBCPQ?cx-by=a2cos.CQBP?=-a2+a2cos.故当 cos=1,即=0,PQ与BC的方向相同时,CQBP?最大,其最大值为0.【巩固训练，问题拓展】1-7CBBDCCB 8、解析(1)由题设知 AB(3,5)，AC(1,1)，则 ABAC(2,6)，ABAC(4,4)所以|ABAC|210，|ABAC|4 2.故所求的两条对角线长分别为42和 210.(2)由题设知 OC(2，1)，ABtOC(3 2t,5t)文档编码:CC3B2D7S3U7 HC9Y6L
45、7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编
46、码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L
47、7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编
48、码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L
49、7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编
50、码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L7I3C1 ZR3E1I4B5O3文档编码:CC3B2D7S3U7 HC9Y6L