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向量既能体现“形”的直观位置特征,又具有“数”的良好运算性质,是数形结合与转换的桥梁和纽带,在学习椭圆内容时要重视由向量运算的几何意义求椭圆方程等问题.例1设G,H分别为非等边三角形ABC的重心与外心,A(0,2),B(0,一2),且GH=AB(λ∈R).(1)求点C(x,y)的轨迹E的方程.(2)过点(2,0)作直线l与曲线E交于点M,N两点,设OP=OM+ON,是否存在这样的直线l,使四边形OMPN是矩形?若存在,求出直线的方程;若不存在,请说明理由.分析:(1)通过向量的共线关系得到坐标的等量
The vector not only reflects the visual position feature of “shape ”, but also has the good computing property of “number ”, which is the bridge and link of the combination and transformation of number form. When studying elliptical content, the importance of the geometric meaning of vector operation (1) Let G and H be the center of gravity and the outer bound of the non-equilateral triangle ABC, A (0,2), B (0, 2), and GH = AB (λ∈R). (1) Find the equation of the trajectory E of point C (x, y). (2) Make the point l and point 2 of the curve E intersect two points M and N, set OP = OM + ON, If there is, find the equation of a straight line; if not, please explain the reason.Analysis: (1) through the collinear relationship between the vectors to get the coordinates of the same amount