Question

已知非零向量a,b满足(向量a-向量b)⊥向量b,且(向量a+2向量b)⊥(向量a-2向量b)求向量a与向量b的夹角

Answer 1

a-b与b垂直,即：(a-b)·b=a·b-|b|^2=0,即：a·b=|b|^2

a+2b与a-2b垂直,即：(a+2b)·(a-2b)=|a|^2-4|b|^2=0

即：|a|^2=4|b|^2,即：|a|=2|b|

故：cos=a·b/(|a|*|b|)=|b|^2/(2|b|^2)=1/2

故：=π/3