向量m=(√3cosB,sinB),n=(sinA,√3cosA),
m*n=√3cosB*sinA+sinB*√3cosA
=√3( cosB*sinA+sinB* cosA)
=√3sin(A+B)
m*n=1+cos(A+B)
所以1+cos(A+B)=√3sin(A+B)
2 [ √3/2 sin(A+B)- 1/2 cos(A+B) ]=1
sin(A+B- 30°) = 1/2
A+B- 30°=30° 或150°
A+B=60°或180°(舍去)
C=120°
(2)
cos120°=(a^2+b^2-c^2)/2ab
-1/2 =(a^2+b^2-12)/2ab
a^2+b^2-12 = - ab (1)
a+b=4 (2)
得:a=b=2