再三角形ABC中,AB=根号3,AC=2,若O为三角形ABC内一点,且满足向量OA+OB+OC=0,则向量AO*向量BC=?_数学解答

再三角形ABC中,AB=根号3,AC=2,若O为三角形ABC内一点,且满足向量OA+OB+OC=0,则向量AO*向量BC=?

人气：497 ℃　时间：2019-09-26 06:42:48

解答

BC = (BA+AC)AO.BC = AO.(BA+AC)= (OB+OC).(BA+AC)( AO=OB+OC)=( OA+AB+OA+AC)(BA+AC)= 2OA.(BA+AC) + |AC|^2 -|AB|^2 = 2OA.BC + 4-33OA.BC = 1OA.BC...3OA*BC=1 为什么不好意思，算错！AO.BC = 2OA.BC + 4-3- OA.BC = 2OA.BC + 13OA.BC = -1OA.BC = -1/3