已知向量a,b满足|a|=3,|a+b|=|a-b|=5,求|b|

|a+b| ^2= (a+b).(a+b)
= |a|^2+2a.b +|b|^2
|a-b|^2=(a-b).(a-b)
= |a|^2-2a.b +|b|^2
|a+b| = |a-b| => a.b =0
|a+b|^2 = 25 = |a|^2 +|b|^2
25 = 9 +|b|^2
|b| = 4