∵(a－b)⊥b
∴(a-b)b=ab-b^2=0
ab=b^2
ab=|b|^2
∵(a＋2b)⊥(a－2b),
∴(a+2b)(a-2b)=a^2-4b^2=0
a^2=4b^2
|a|^2=4|b|^2
|a|=2|b|
cos(a,b)=ab/|a||b|
=|b|^2/2|b||b|
=1/2
∴向量a与b的夹角是60°