新建、改建金融机构营业场所金库50

1、9.5空间向量及其运算2.共线向量与共面向量一.复习提问:2.平面向量共线的充要条件.3.平面向量的根本定理.1.共线向量.二.新课:1.共线向量定理: 对于空间任意两个向量a、b(b=0),a/b的充要条件是存在实数使a= b.推论：如果l为经过点A且平行于非零向量a的直线，那么对任一点O，点P在直线l上的充要条件是存在实数t，满足等式OP = OA + t a. (1)其中向量a叫做直线l的方向向量.aPBOP = (1- t)OA + t OB. (2)说明: (1),(2)都叫做空间直线的向量参数表示式.2.共面向量(1).平面与向量a,如果向量a所在的直线OA平行于平面或向量a在平面

2、内,那么我们就说向量a平行于平面,记作a/ .aaOA(2)共面向量:平行于同一平面的向量 思考:空间任意两个向量是否一定共面? 空间任意三个向量哪?ABCDMaAbBA(3)共面向量定理:如果两个向量a、b不共线，那么向量p与向量a、b共面的充要条件是存在实数对x、y，使P = xa + yb.推论:空间一点P位于平面MAB内的充分必要条件是存在有序实数对x、y，使pPMP = xMA + yMB或对空间任一定点O，有OP = OM + xMA + yMB.三.例题例1 对空间任意一点O和不共线的三点A、B、C，试问满足向量关系式OP = xOA + yOB + zOC（其中x+y+z=1）

3、的四点P、A、B、C是否共面。例2 已知平行四边形ABCD，从平面AC外一点O引向量OE = kOA，OF = kOB，OG = kOC，OH = kOD，求证：（1）四点E、F、G、H共面；（2）平面EG/平面AC.谢谢合作！再见！UiYl!p*s+wA.D1H4L8OcSfWjZm%q(u=xC0G3K7NaReUiYl$p*t+wA.E1H4L8OcSfWjZn%q)u=yC0G3K7NbReViYm$p(t+wA.E1H5L8PcSgWj#n%q)u=yD0G4K7ObRfViYm$p(t+xA;E1I5L9PcSgWj#n%r)uyC:F3J6MaQdUhXl!o*s-wz.D0H4

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