Question

非零向量a,b满足2a*b=(a^2)*(b^2),|a|+|b|=2 ,则a与b的夹角的最小值是多少

Answer 1

let a与b的夹角 =x 2a.b = |a|^2|b|^22|a||b|cosx = |a|^2|b|^2cosx = |a||b|/2= |a|( 2-|a|) /2(cosx)' = 1 - |a| =0|a| =1(cosx)'' = -1 min xmin x at |a| =1cos x = |a|( 2-|a|) /2min x = arccos( 1/2)= π/3a...