新建、改建金融機構(gòu)營業(yè)場所金庫50

1、9.5空間向量及其運算2.共線向量與共面向量一.復習提問:2.平面向量共線的充要條件.3.平面向量的根本定理.1.共線向量.二.新課:1.共線向量定理: 對于空間任意兩個向量a、b(b=0),a/b的充要條件是存在實數(shù)使a= b.推論：如果l為經(jīng)過點A且平行于非零向量a的直線，那么對任一點O，點P在直線l上的充要條件是存在實數(shù)t，滿足等式OP = OA + t a. (1)其中向量a叫做直線l的方向向量.aPBOP = (1- t)OA + t OB. (2)說明: (1),(2)都叫做空間直線的向量參數(shù)表示式.2.共面向量(1).平面與向量a,如果向量a所在的直線OA平行于平面或向量a在平面

2、內(nèi),那么我們就說向量a平行于平面,記作a/ .aaOA(2)共面向量:平行于同一平面的向量 思考:空間任意兩個向量是否一定共面? 空間任意三個向量哪?ABCDMaAbBA(3)共面向量定理:如果兩個向量a、b不共線，那么向量p與向量a、b共面的充要條件是存在實數(shù)對x、y，使P = xa + yb.推論:空間一點P位于平面MAB內(nèi)的充分必要條件是存在有序?qū)崝?shù)對x、y，使pPMP = xMA + yMB或?qū)臻g任一定點O，有OP = OM + xMA + yMB.三.例題例1 對空間任意一點O和不共線的三點A、B、C，試問滿足向量關系式OP = xOA + yOB + zOC（其中x+y+z=1）

3、的四點P、A、B、C是否共面。例2 已知平行四邊形ABCD，從平面AC外一點O引向量OE = kOA，OF = kOB，OG = kOC，OH = kOD，求證：（1）四點E、F、G、H共面；（2）平面EG/平面AC.謝謝合作！再見！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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