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平面向量的基本定理指出:如果→OP1,→OP2是同一平面内的两个不共线的向量,那么对于这个平面内的任一向量OP,有且仅有一对实数x,y,使→OP=x→OP1+y→OP2(x,y∈R).此定理处于平面向量知识的核心地位,是几何问题向量化的理论基础.它说明了只要在平面内取定一组基底,那么平面内的任一向量都可用这组基底进行唯一的线性表示,这个过程充分地体现了数学化的过程,其形式化表达展现了数学结构体系的严谨性和逻辑性.
The basic theorem of the plane vector states that if →OP1, →OP2 are two non-collinear vectors in the same plane, then for any vector OP in this plane, there is only one pair of real numbers x, y, so that → OP =x→OP1+y→OP2(x,y∈R). This theorem is at the core of the knowledge of the plane vector and is the theoretical basis for the vectorization of geometric problems. It shows that as long as a set of bases are determined in a plane, then the plane Any vector within can use this set of bases to perform a unique linear representation. This process fully embodies the process of mathematics. Its formal expression expresses the rigor and logic of the mathematical structural system.