Question

已知a=(sinx,cosx),b=(1,-1)

(1)若<a,b>=π/2,求x
（2）求|a-b|的最大值

Answer 1

(1)sinx-cosx=0
sinx=cosx
x=排/4
(2)a-b=(sinx-1,cosx+1)
|a-b|=√[(sinx-1)^2+(cosx+1)^2]
|a-b|=√[sin^2x+1-2sinx+cos^2x+1-2cosx]
|a-b|=√[3-2(sinx+cosx)]
|a-b|=√[3-2√2sin(x+排/4)]
|a-b|最大=√(3+2√2)