江画工太猩院 关于数量积的说明 (1)·l 证∵6=0,∴·=l|dic0s6 (2)ab=0→aLb. 证(→):a·b=0,≠0,b≠0 cos6=0,=π,:l⊥b. (=):l⊥b,:6= c0s6=0 lb=l‖b|c0s6=0.江西理工大学理学院 关于数量积的说明： ( 2 ) a ⋅ b = 0 r r ⇐ ⇒ a b . r r ⊥ ( ⇒ ) a ⋅ b = 0 , r r Q | a |≠ 0 , r | b |≠ 0 , r ∴cos θ = 0 , a b . r r ∴ ⊥ ( 1 ) | | . 2 a a a r r r ⋅ = ( ⇐ ) a b , r r Q ⊥ ∴cos θ = 0 , a ⋅ b =| a || b | cos θ = 0 . r r r r Q θ = 0 , | || | cos | | . 2 a a a a a r r r r r 证 ∴ ⋅ = θ = 证 θ = , 2 π , 2 π ∴ θ =