www.91887.com:2019(北师大版)数学必修四:2.6《平面向量数量积的坐标表示》ppt课件(2)_图文

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精品数学课件 2019 年 北 师 大 版 平面向量数量积坐标的表示 设两个非零向量 a ? (x1 , y1 ),b ? (x2 , y 2 ) a ? b ? x1 x2 ? y1 y2 (1)设a ? ( x, y ), 则 | a |? x2 ? y 2 设表示 a的 有 向 线 段 的 起 点 和 点 终的 坐标分别为( x1 , y 1 ), ( x 2 , y 2 ), 那 么 | a |? ( x1 ? x 2 ) 2 ? ( y 1 ? y 2 ) 2 ( 2)设a ? ( x1 , y 1 ), b ? ( x 2 , y 2 ), 则 a ? b ? x1 x 2 ? y 1 y 2 ? 0 a // b ? x1 y 2 ? x 2 y 1 ? 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 y B 标. O AB 的坐 A 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.

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