(Ⅱ)∵ =(1,1,m), =(-1,1,m), ∴||=||, 又已知∠ACB=60°,∴△ABC为正三角形,AC=BC=AB=2. 在Rt△CNB中,NB=, 可得NC=,故C(0,1, ).
连结MC,作NH⊥MC于H,设H(0,λ, λ) (λ>0). ∴=(0,1-λ,-λ),
=(0,1, ). ・ = 1-λ-2λ=0, ∴λ= ,
∴H(0, , ), 可得=(0,, - ), 连结BH,则=(-1,, ),
∵・=0+ - =0, ∴⊥, 又MC∩BH=H,∴HN⊥平面ABC,
∠NBH为NB与平面ABC所成的角.又=(-1,1,0),
∴cos∠NBH= = =
- 答案