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向量具有代数和几何的双重身份,融数形于一体。而解析几何是将数与形结合在一起,故向量与解析几何有着密切的联系。而解析几何用常规解法往往运算比较繁琐,运用向量作为工具可起到化难为易,化繁为简的效果,使学生开拓思路,减轻负担。下面就几个方面看看向量在解析几何中的应用。一、向量和差运算与线段中点的结合例1.设A,B是抛物线y2=2x+8上两点,O为坐标原点,且OP=OA+OB2,点P的坐标为(0,1),求直线A B的斜率。
Vectors have dual identities of algebra and geometry, and they are integrated into one. Analytic geometry is a combination of numbers and shapes, so vectors and analytical geometry are closely linked. Analytic geometry using conventional solutions tends to be cumbersome to calculate. Using vector as a tool can make it easier to change the complexity and simplify the results, so that students develop ideas and reduce the burden. Let’s take a look at the application of vectors in analytical geometry in the following sections. First, the combination of vector and difference operations and the midpoint of the line segment 1. Let A, B be two points on the parabola y2=2x+8, O is the origin of coordinates, and OP=OA+OB2, the coordinates of point P is (0, 1) Find the slope of the straight line AB.