2022年人教A版高中数学必修四2.4《平面向量的数量积》导学案2 .pdf
名师精编优秀教案高中数学人教版必修4：2.4 平面向量的数量积导学案【学习目标】1、知道平面向量数量积的含义及其物理意义；2知道平面向量数量积积与投影的关系；3、会运用平面向量的数量积及其运算律.【重点难点】重点：向量数量积的定义及运算律难点：数量积的应用【知识链接】1、向量的线性运算；2、向量),(11yxa，),(22yxb共线01221yxyx.【学习过程】阅读课本第103 页到第 105 页的内容，尝试回答以下问题：知识点 1:平面向量数量积的物理背景及其含义问题 1物体在 力 F 作用下产生位移S，那么力F 所做的功_W.力和位移是矢量，功是 标量，类比我们引入两个向量的数量积的概念：已知两个非零向量a与b，我们把 _叫做a与b的数量积,记作ab，即 _ _,其中是a与b的夹角.问题 2、请叙述投影的定义.问题 3、由投影的定义，你能叙述ba的几何意义吗？问题 4设a与b是非零向量则：（1）_ba；（2）当a与b同向时，ba=_；当a与b反向时，ba=_.特别地aa=_,a=_;名师精编优秀教案（3）baba_；（4）babacos.问题 6、尝试用数量积的运算律证明下列等式：（1）2222abaa bb；（2）22ababab；例 1、已知5a，2b，a与b的夹角为120，求23abab的值.知识点 2:平面向量数量积的坐标表示，模，夹角阅读课本第106 页到 107 页的内容，尝试回答以下问题：问题 1、已知两个非零向量),(11yxa，),(22yxb，怎样用a与b的坐标表示ba呢？（提示：jyixa11，jyixb22）问题 2由问题1，若),(yxa，则2a=_，或a=_.问题 3、如果),(11yxa，),(22yxb，是a与b的夹角，则_cos.例 2、在ABC中，已知)2,1(A，)1,3(B，)2,5(C，求BACACABcos,.文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 ZZ7R7S1Q2Y2文档编码:CV2Z9Q3Y9Y9 HL2Z7V7S1Q2 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