若a、b是两个非零向量,且|a|=|b|=λ|a+b|,λ∈ ,则b与a-b的夹角的取值范围是 　　　　 .

设b与a-b的夹角为θ,∵λ|a+b|=|b|,|a|=|b|,∴λ 2 (a 2 +2a?b+a 2 )=a 2 ,∴a?b= a 2 ,又|a-b| 2 =a 2 -2a?b+a 2 =2a 2 - a 2 =(4- )a 2 .而cos θ= = = = =- =- .由 ≤λ≤1得1≤ ≤3,∴- ≤- ≤- ,∴- ≤cos θ≤- ,∴ ≤θ≤ .