1、2.4.1 平面向量数量积的物理背景及其含义baba a12FS2SFFS2FS2SFSFba2ba|a|bcosabcos|baabba cos|babaab2cos|baba3ba 20?2?200310ACB 2 2已知正三角形已知正三角形ABCABC的边长为的边长为1 1,求:,求:(1 1);(2 2);(3 3).ACAB BCAB BCAC6021120216021baabbaabbaaaab|ba|ba2|a2|aaaa0ba|ba|bacos|baba2a判定两向量垂直判定两向量垂直用于计算向量的模用于计算向量的模用于计算向量的夹角用于计算向量的夹角,以以及判断三角形的形状及
2、判断三角形的形状.4abbaba acos|baba2bOAaBB1abba5cos|baba?B1aAB1aAO0cos|?b0cos|?b0cos|?b5aAOOaA00cos|?bbBB1OaAB10cos|?bObBbBbBbBba a|abacos|b5cos|baba?交换律交换律结合律结合律分配律分配律baab)()(bcacabbcaccba)(abbabababa)()()()(cbacbacbcacba)(5交换律交换律结合律结合律分配律分配律abbabababa)()(cbcacba)(52222)(bbaaba22)()(bababa2)(ba bbabbaaa222bbaa)()(bababbabbaaa-22ba)()(baba66|a4|babo60)3()2(baba)3()2(bababbbaaa622|6|bbaa22|660cos|bbaa22462146672670baabaa000baab0ccbcabaA AC CB B7ABC4BCBCBAACAB880baba2|aaaa|cosbaba 8cos|baba0a0babbabababa)()(cbcacba)(ba a|abacos|b8