Question

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

Answer 1

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 + 4-3

3OA.BC = 1

OA.BC = 1/3