[2016年高三数学理创新设计资料包5-3.ppt

必威体育精装版考纲　1.理解平面向量数量积的含义及其物理意义； 2.了解平面向量的数量积与向量投影的关系；3.掌握数量积的坐标表达式，会进行平面向量数量积的运算；4.能运用数量积表示两个向量的夹角，会用数量积判断两个平面向量的垂直关系． 第3讲 平面向量的数量积 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1．平面向量的数量积 (1)定义：已知两个非零向量a与b，它们的夹角为θ，则数 量_________ 叫作a与b的数量积(或内积)，记作a·b，即 a·b＝_________，规定零向量与任一向量的数量积为0， 即0·a＝0. (2)几何意义：数量积a·b等于a的长度|a|与b在a的方向上的投影_______的乘积． 知 识 梳 理 |a||b|cos θ |a||b|cos θ |b|cos θ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2．平面向量数量积的性质及其坐标表示 设向量a＝(x1，y1)，b＝(x2，y2)，θ为向量a，b的夹角． (1)数量积：a·b＝|a||b|cos θ＝x1x2＋y1y2. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3．平面向量数量积的运算律 (1)a·b＝b·a(交换律)． (2)λa·b＝λ(a·b)＝a·(λb)(结合律)． (3)(a＋b)·c＝a·c＋b·c(分配律)． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 诊 断 自 测 × √ √ × × Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 答案　A Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解析　因为2a－3b＝(2k－3，－6)，由(2a－3b)⊥c，所以(2a－3b)·c＝2(2k－3)－6＝0，解得k＝3，选C. 答案　C Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 答案　90° Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 5．(人教A必修4P104例1改编)已知|a|＝5，|b|＝4，a与b的夹角θ＝120°，则向量b在向量a方向上的投影为_______． 解析　由数量积的定义知，b在a方向上的投影为： |b|cos θ＝4×cos 120°＝－2. 答案　－2 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 深度思考　对于第(2)小题同学们首先想到的方法是什么？这里提醒同学们此题可有三种解法：法一利用定义；法二利用向量的坐标运算；法三利用数量积的几何意义，你不妨试