向量b与非零向量a共线的充要条件是有且只有一个非零实数λ,使得b=λa。向量平行的坐标条件:在平面直角坐标系中,向量b=(b1,b2)与a=(a1,a2)(a1,a2不同时为零)平行的充要条件是a1b2-a2b1=0。若a1,a2都不为零,则b1/a1=b2/a2。此定理为解决涉及三点共线和两直线(或线段)平行问题提供了一种方法,现举例如下:一、求点的坐标 The necessary and sufficient conditions for collinearity between vector b and nonzero vector a are that there is only one nonzero real number λ such that b = λa. Vector Parallel Coordinate Conditions: The necessary and sufficient condition that the vector b = (b1, b2) is parallel to a = (a1, a2) (a1 and a2 are both non-zero) is a1b2-a2b1 = 0 in a rectangular coordinate system. If a1, a2 are not zero, then b1 / a1 = b2 / a2. This theorem provides a method for solving the problem of three-point collinearity and two straight lines (or line segments) parallelism, for example as follows: First, find the coordinates of the point