已知向量a=（cos3x/2,sin3x/2）,向量b=（cosx/2,-sinx/2）,向量c=（根号3,-1）

(1)
a⊥b
=> a.b=0
(cos(3x/2),sin(3x/2).(cos(x/2),-sin(x/2))=0
cos(3x/2)cos(x/2)-sin(3x/2)sin(x/2)=0
cos2x=0
2x = nπ+π/2
x = nπ/2 + π/4 n=0,1,2,...
x的值的集合 = { x | x= nπ/2 + π/4,n=0,1,2,.}
(2)
a-c = ( cos(3x/2)-cos(x/2),sin(3x/2)+sin(x/2))
|a-c|^2
= (cos(3x/2)-cos(x/2))^2+ (sin(3x/2)+sin(x/2))^2
= 2 -2(cos(3x/2)cos(x/2))- (sin(3x/2)+sin(x/2))
= 2-2cos2x
|a-c|^2的最大值 at cos2x =-1
max |a-c| = 2