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www118com:高中数学北师大版必修4第二章《平面向量数量积的坐标表示》ppt课件2_图文

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平面向量数量积坐标的表示

设两个非零向量a ? (x1, y1),b ? (x2, y2 ) a ? b ? x1x2 ? y1 y2
(1)设a ? (x, y),则 | a |? x2 ? y2
设 表 示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 ? y 2 )2
(2)设a ? (x1 , y1 ),b ? (x2 , y 2 ),则
a ? b ? x1x2 ? y1y2 ? 0
a // b ? x1y2 ? x2y1 ? 0

例题1.求等腰直角三角形中两直角边上的中线所 成的钝角的度数。

课堂练习已知△ABC的顶点坐标为A(1,1), B(4,1),C(4,5),用向量计算cosA , cosB , cosC.

例题2.如图,以原点和A(5,2)为两个顶点作等腰

直角三角形OAB,∠B=90°,求点B和 AB 的坐

标.

yB

A

O

x

课堂练习:已知△ABC的顶点坐标为A(2,-1),

B(3,2) ,C(-3,-1),BC边上的高为AD,求D点

及 AD 的坐标.

D(1,1), AD ? (?1,?2)

例题3.已知直角梯形ABCD中,AB//CD, ∠CDA=∠DAB=90°,CD=DA=0.5AB, 求证:AC⊥BC

例题4.已知三点A(2,1),B(3,2),D(-1,4),
(1)求证:AB ? AD

(2)要使四边形ABCDA为矩形,求点C的坐标并求矩形ABCD两对角 线所成的锐角.

课堂练习:如果正方形OABC的边长为1,点D、E 分别为AB、BC的中点,试求cos∠DOE.

编后语
? 老师上课都有一定的思路,抓住老师的思路就能取得良好的学习效果。在上一小节中已经提及听课中要跟随老师的思路,这里再进一步论述听课时如何 抓住老师的思路。
? ① 根据课堂提问抓住老师的思路。老师在讲课过程中往往会提出一些问题,有的要求回答,有的则是自问自答。一般来说,老师在课堂上提出的问 题都是学习中的关键,若能抓住老师提出的问题深入思考,就可以抓住老师的思路。
? ② 根据自己预习时理解过的逻辑结构抓住老师的思路。老师讲课在多数情况下是根据教材本身的知识结构展开的,若把自己预习时所理解过的知识 逻辑结构与老师的讲解过程进行比较,便可以抓住老师的思路。
? ③ 根据老师的提示抓住老师的思路。老师在教学中经常有一些提示用语,如“请注意”、“我再重复一遍”、“这个问题的关键是····”等等,这些 用语往往体现了老师的思路。来自:学习方法网
? ④ 紧跟老师的推导过程抓住老师的思路。老师在课堂上讲解某一结论时,一般有一个推导过程,如数学问题的来龙去脉、物理概念的抽象归纳、语 文课的分析等。感悟和理解推导过程是一个投入思维、感悟方法的过程,这有助于理解记忆结论,也有助于提高分析问题和运用知识的能力。
? ⑤ 搁置问题抓住老师的思路。碰到自己还没有完全理解老师所讲内容的时候,最好是做个记号,姑且先把这个问题放在一边,继续听老师讲后面的 内容,以免顾此失彼。来自:学习方法网
? ⑥ 利用笔记抓住老师的思路。记笔记不仅有利于理解和记忆,而且有利于抓住老师的思路。

2019/8/29

最新中小学教学课件

11

谢谢欣赏!

2019/8/29

最新中小学教学课件

12


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