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

Question

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

Answer 1

(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)/(39+12根号3)
题目是2又根号3/3丨a丨?