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agks2201com: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4

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课题: 平面向量数量积的坐标表示、模、夹角

[课时安排]

1 课时

[教学目标]

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]

平面向量数量积的坐标表示的应用

[教学难点]

平面向量数量积的坐标表示的综合运用

[教学器材]

[教法学法]

[教学过程]

备注

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 ? x1x2 ? y1 y2 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 , y2 ) ,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

? x1x2 ? y1 y2 ? 0

④ 两 向 量 夹 角 的 余 弦 ( 0?? ?? )

cos

= a?b ?
| a |?|b|

x1 x2 ? y1 y2 x12 ? y12 x2 2 ? y2 2

2.教学例题.

1

小中高学习资料 推荐下载

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, , b 角θ (精确到 1o)

, ,求 a·b 及 a 、 b 间的夹

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]

养成良好的学习惯,有利于激发生积极性和主动;形策略提高效率培自能力创新精神造使终身受益Mr.Johnsadevbupifltc,在教师讲课之前己先独立地阅读内容。初步理解是上做接知识准备过程些由没预对老一堂要无所坐等wygF加油就会功命不息

2


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