在向量的学习中,经常会遇到在形如OP=xOA+yOB的条件下研究x,y的关系,解题关键就是如何使向量的条件实数化.而这样转化的思路有许多向量工具可以应用.下面从三个方面研究如何透彻的研究条件的特点并形成解决问题的策略.1.定基底,二边算当条件中出现“OP=xOA+yOB”时,易想到平面向量基本定理:平面内的所有向量都可以用不共线向量OA,OB的线性组合来表示,并且这样的表示是唯一的,即存在唯一的实数对(x,y),使得OP=xOA+yOB成立.反之 In the study of vectors, we often encounter the relationship between x and y in the form of OP = xOA + yOB, and the key to solve the problem is how to realize the conditions of the vector, and there are many vector tools Application of the following three aspects of research on how to thoroughly study the characteristics of the conditions and the formation of strategies to solve the problem.1, given the base, both sides of operator conditions appear “OP = xOA + yOB ”, easy to think of basic vector Theorem: All vectors in a plane can be represented by a linear combination of non-collinear vectors OA and OB, and such a representation is unique. That is, there exists a unique pair of real numbers (x, y) such that OP = xOA + yOB holds .on the contrary