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2019-2020学年高中数学第二章平面向量2.3平面向量数量积 的坐标表示模夹角教案新人教A版必修
[课时安排] [教学目标] 1 课时 1.知识与技能: 使学生掌握平面向量数量积的坐标表示, 掌握向量垂直的坐标表示的条件,及平面内两点间的距离公 式,能用所学知识解决有关综合问题 2.过程与方法: 启发式教学,引导学生思路 3. 情感、 态度与价值观: 经历由实际问题建立数学模型的 过程,体会其基本方法. [教学重点] [教学难点] [教学器材] [教法学法] [教学过程] 一、复习准备: 1.平面向量的数量积的物理背景及其含义? 2.向量的数量积的几何意义. 3.平面向量数量积的运算律. 二、讲授新课: 1.教学坐标表示. ① 平面两向量数量积的坐标表示: 两个向量的数量积等于它们对应坐标的乘 积的和.即 a ? b ? x1 x2 ? y1 y 2 ② 平面内两点间的距离公式: 如果表示向量 a 的有向线段的起点和终点的坐 标分别为 ( x1 , y1 ) 、 ( x2 , y 2 ) ,那么 | a |? ( x1 ? x2 )2 ? ( y1 ? y2 )2 ③ 向 量 垂 直 的 判 定 : 设 a ? ( x1 , y1 ) , b ? ( x2 , y2 ) , 则 a ? b 备注 平面向量数量积的坐标表示的应用 平面向量数量积的坐标表示的综合运用

? x1 x2 ? y1 y 2 ? 0
④ = 两 向 量 夹 角 的 余 弦 (
? x1 x 2 ? y1 y 2 x1 ? y1
2 2

0 ?? ??



cos

a ?b | a |?| b |

x2 ? y2

2

2

2.教学例题.

① 讲解例 5:已知 A(1, 2),B(2, 3),C 并给出证明

, 5),试判断△ABC 的形状,

练习:在△ABC 中, AB =(2, 3), AC =(1, k),且△ABC 的一个内角为 直角,求 k 值. (学生板演→教师修正→学生修正) ② 讲解例 6:设 a = (5, 角θ (精确到 1 ) 练习:已知 A(1,0),B(3,1),C(2,0),且 a = BC , a = CA ,则 a 与 b 的 夹角为多少? (学生板演→教师修正→学生修正) 3.小结: 平面内两点间的距离公式;向量垂直的判定;两向量夹角的余弦. [教学反思]
o

,b



,求 a·b 及 a 、 b 间的夹


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