(1) 向量a=（cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),
向量a+向量b=(cos3/2x+cosx/2,sin3/2x-sinx/2)
| 向量a+向量b|=[(cos3/2x+cosx/2)²+(sin3/2x-sinx/2)²]½
=(cos²3/2x+2cos3/2x·cosx/2+cos²x/2+sin²3/2x-2sin3/2x·sinx/2+sin²x/2)½
=(2cos3/2x·cosx/2-2sin3/2x·sinx/2+2)½
=(2cos2x+2)½=[2(2cos²x-1)+2]½=[4cos²x]½
∵x屬于[0,π\(zhòng)2],∴cosx>0 ∴ |向量a+向量b|=2cosx
(2) 向量a.向量b=(cos3/2x,sin3/2x)·(cosx/2,-sinx/2)
=cos3/2x·cosx/2－sin3/2x·sinx/2
=cos2x
∴f(x)=向量a.向量b-4|向量a+向量b|
=cos2x-8cosx
=2cos²x-1-8cosx
令cosx=t,t屬于[0,1]
y=2t²-8t-1,t屬于[0,1]
對(duì)稱軸為t=2
當(dāng)t=1時(shí),y有最小值-7
∴[f(x)]min=-7