(1)依题意,∵向量a×向量b=0-π/2＜θ＜π/2∴sinθ+cosθ=0根号2sin(θ+π/4)=0-π/4＜θ+π/4＜3π/4∴θ+π/4=0θ=-π/4(2)依题意,∵向量a+向量b=(1+sinθ,1+cosθ)∴|向量a+向量b|=根号(sin²...