平面向量的基本定理是平面向量坐标表示的基础,说明了同一平面内任一向量都可以表示为两个不共线向量的线性组合.即:如果e_1,e_2是同一平面内的两个不共线向量,那么对于这一平面内的任一向量a,有且只有一对实数λ_1,λ_2,使a=λ_1e_1+λ_2e_2.这一对有序实数决定了向量a与基底向量e_1,e_2的位置关系.下面就实数λ_1,λ_2的变化所反映的向量a与基底向量e_1,e_2的几种位置关系作一些初 The basic theorem of plane vector is the basis of plane vector coordinate representation, which shows that any one vector in the same plane can be expressed as a linear combination of two non-collinear vectors, that is, if e_1 and e_2 are two non-co-planar vectors Line vector, then for any vector a in this plane, there is only one pair of real numbers λ_1, λ_2 such that a = λ_1e_1 + λ_2e_2. This pair of ordered real numbers determines the positions of vector a and base vectors e_1, e_2 The following relationship between the vector a and the substrate vectors e_1, e_2 reflected by the change of real numbers λ_1 and λ_2