已知a,b是单位向量,ab的向量积=0,若向量c满足|c-a-b|=1,则C的取值范围是?

|c-(a+b)|^2=|c|^2+|a+b|^2-2c·(a+b)=|c|^2+2-2sqrt(2)|c|cos=1即：cos=(|c|^2+1)/(2sqrt(2)|c|)∈[-1,1](|c|^2+1)/(2sqrt(2)|c|)≤1,可得：sqrt(2)-1≤|c|≤sqrt(2)+1(|c|^2+1)/(2sqrt(2)|c|)≥-1自动满足,不用解...