分析:若两向量a,b垂直,则它们的数量积a•b = 0
反过来,也可作为垂直的判定条件.
已知:OA⊥BC,OB⊥AC
则:OA•BC=0
OA•(OC - OB) = 0
OA•OC - OA•OB = 0 (1)
同量,OB•AC = 0
OB•(OC - OA) = 0
OB•OC - OB•OA = 0 (2)
(2) - (1):OB•OC - OB•OA - OA•OC + OA•OB = 0
OB•OC - OA•OB - OA•OC + OA•OB = 0
OB•OC - OA•OC = 0
OC•(OB - OA) = 0
OC•AB = 0
所以OC⊥AB.