高数课程妥媒血课件 镭理工大理>> 关于数量积的说明: (1)a·a=a2. 证∵日=0,∷a·a=l‖lcosθ=a2 (2)a·b=0←→⊥b 证(→):a·b=0,|d≠0,|b|≠0, Cos0=0 2 alb (÷):db,6 cos 6=0, 2 n·b=a‖b|cos6=0. Http://www.heut.edu.cn(2) a  b = 0    a b.   ⊥ () a  b = 0,    | a | 0,  | b | 0,  cos = 0, a b.    ⊥ (1) | | . 2 a a a     = () a b,    ⊥ cos = 0, a  b =| a || b | cos = 0.      = 0, | || | cos | | . 2 a a a a a      证   =  = 证  = , 2  , 2   = 关于数量积的说明：