已知a,b是非零向量且满足(a-2b)⊥a,(b-2a)⊥b则a与b的夹角是多少

(a-2b)⊥a得a^2-2ba=0.a^2=2ab,|a|^2=2ab.
(b-2a)⊥b得b^2-2ba=0.b^2=2ab,|b|^2=2ab.
ab=|a||b|cosx
cosx=ab/(|a||b|)=ab/2ab=1/2
x=60度