Question

已知向量OB=(1,1),|向量OA-(2,0)|=1,求向量AB最大值是

Answer 1

设：OA=(x,y),则：OA-(2,0)=(x,y)-(2,0)=(x-2,y),即：(x-2)^2+y^2=1

即A点的轨迹是一个圆,设：x=2+cost,y=sint

AB=OB-OA=(x,y)-(1,1)=(x-1,y-1),则：|AB|^2=(x-1)^2+(y-1)^2

=(1+cost)^2+(sint-1)^2=3-2(sint-cost)=3-2sqrt(2)sin(x-π/4)

故|AB|^2的最大值：3+2sqrt(2),即|AB|的最大值：sqrt(2)+1