已知非零向量a,b满足丨a+b丨=丨a-b丨=2又根号3/3丨a丨,则a+b与a-b的夹角为

(a+b).(a-b)=|a|^2-|b|^2 |a+b|^2=|a-b|^2 |a|^2+|b|^2+2a.b=|a|^2+|b|^2-2a.b a.b=0 a与b垂直 |a+b|^2=|a|^2+|b|^2=(6+根号3)^2/9|a|^2根号3 |b|^2=(30-12根号3)/9|a|^2 (a+b).(a-b)=|a|^2-|b|^2=(12根号3-21)/9|a|^2 cosa=(a+b).(a-b)/|a+b|^2=(12根号3-21)&