已知向量a=[cos(3x/2),sin(3x/2)],向量b=[cos(x/2),-sin(x/2)],且x[0,π/2](1)求|向量a+向量b| (2)求函数f(x)=向量a*向量b-4|向量a+向量b|的最小值
问题描述：
已知向量a=[cos(3x/2),sin(3x/2)],向量b=[cos(x/2),-sin(x/2)],且x[0,π/2]
(1)求|向量a+向量b| (2)求函数f(x)=向量a*向量b-4|向量a+向量b|的最小值
答
|向量a+向量b|=|cos(3x/2)+cos(x/2),sin(3x/2)-sin(x/2)|=[cos(3x/2)+cos(x/2)]^2+[sin(3x/2)-sin(x/2)]^2=[cos(3x/2)]^2+[cos(x/2)]^2+[sin(3x/2)]^2+[sin(x/2)]^2=2 cos(3x/2)cos(x/2)-sin(3x/2)sin(x/2)-4*2=cos(2x)-8=-9