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有关平面向量中OC=xOA+yOB经常出现在高考及各地区的模拟试卷中,但多数试题考查平面向量共线定理:在平面中,A、B、C三点共线的充要条件是OC=xOA+yOB(O为平面内不在直线AB上的一点),且x+y=1.平面向量共线定理可以判断点C在直线AB上,笔者进一步探究发现可以用OC=xOA+yOB表示点C与直线AB的位置关系、及点C所在的平面区域,供大家参考.
OC = xOA + yOB in plane vectors often appear in the entrance examinations and various sections of the simulation papers, but most of the questions examine the collinearity theorem of plane vectors: in the plane, A, B, C three-point collinear if and only if OC = xOA + yOB (O is a point in the plane is not on the straight line AB), and x + y = 1. Plane vector collinear theorem can determine the point C in the straight line AB, the author further exploration found that OC = xOA + yOB Point C and the linear relationship between the location of AB, and the plane C where the region for your reference.