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wwwfsymsmcom:河北省二十冶综合学校高中分校高中数学必修四:2.4.2平面向量数量积的坐标表示模夹角导学案

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§2.4 。2 平面向量的数量积的坐标表示、模、夹角 【学法指导】 :认真自学,激情讨论,愉快收获。●为必背知识 【学习目标】 :掌握向量数量积运算的坐标表示,模的坐标表示,及夹角的坐标表示 【学习重点】 :向量数量积运算的坐标表示,模的坐标表示,及夹角的坐标表示 【学习难点】 :向量数量积运算的坐标表示,模的坐标表示,及夹角的坐标表示 【教学过程】 : 一, 知识回顾 (1) a ? b = (3) a = 。 。 (2) a = (4) a ? b ? (6) a ? b a - b = 2 。 。 。 (5) a ? b 2 = (7)若 a ? ( x1 , y1 ) , b ? ( x2 , y2 ) ? ? ? ?? ? a ? b= ,a ?b= , , (8)若 a ? ( x, y) 和实数 ? ,则 ? a ? 二,探究新知 (1) 已知两个非零向量 a ? ( x1 , y1 ) , b ? ( x2 , y2 ) 则a ?b= (2)若 a ? ( x, y) ,则 a 2 2 。 ? a ? a?a ? ,所以, a = 。 如果表示向量 a 的有向线段的起点和终点的坐标分别为 A(x1 , y1 ) , B(x 2 , y 2 ) 则 a ? AB ? , a = AB = 。 。 (3)设 a ? ( x1 , y1 ) , b ? ( x2 , y2 ) ,则 a ? b ? a ? b ? 0 ? (4)设向量 a 和 b 都是非零向量, ? 为它们的夹角。 则因为 a ? b ? a ? b ? cos? ,所以 cos ? = 若 a ? ( x1 , y1 ) , b ? ( x2 , y2 ) 则 cos ? = , 。 三,典型例题 例1, 107 页课本练习 1 例2, a ? (2,1) , b ? (1,3) ,求 a ? b ,及 a 与 b 的夹角 ? 例3, 107 页课本练习 2 例4, 已知 A(1,2) ,B(2,3)C(-2,5)试判断△ABC 的形状,并给予证明。 例5, 已知 A(-1,-4) ,B(5,2)C(3,4)试判断△ABC 的形状,并给予证明 例 6 求证:A(1,0) ,B(5, -2) ,C(8,4) ,D(4,6)为顶点的四边形是一个矩形。

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