(1)
a垂直c
=> a.c =0
(cosx,sinx).(siny,cosy)=0
cosxsiny+ sinxcosy =0
sin(x+y) =0
x+y = k(180°) k =0,1,2,..
2(x+y) = k(360°)
cos(2x+2y) = cosk(360°) = 1
(2)
if a // b
=>cosx/sinx=(cosx+2√3)/sinx
cosx =cosx+2√3
0 = 2√3 ( contradiction)
=> a和b不可能平行
(3)
F(x) = a.(b-2c)
= ( cosx.sinx).(cosx+2√3 ,sinx-2)
= (cosx)^2+2√3 cosx + (sinx)^2-2sinx
= 4(√(3/2)cosx- (1/2)sinx) +1
= 4sin(60°-x) +1
max F(x) at x = -30°
max F(x) = 5