平面向量的线性运算O是三角形ABC内一点,满足向量OA+向量OB+向量OC=0,|向量OA|=|向量OB|=|向量OC|,求证△A_数学解答

人气：446 ℃　时间：2020-02-18 08:18:06

解答

let|OA|=|OB|=|OC| = kOA+OB+OC = 0OA.OA = (OB+OC).(OB+OC)k^2 = 2k^2 +2OB.OC=> OB.OC = -k^2/2similarlyOC = -(OA+OB)OA.OB = -k^2/2andOC.OA = -k^2/2AB = OB-OA|AB|^2 = (OB-OA).(OB-OA)= |OB|^2+ |OA|^2 - 2OB...