(1)
|a|^2= (2A+B).(2A+B) = 4|A|^2+|B|^2+ 4|A||B|cos60° = 4+1+2 = 7
|a|= √7
|b|^2= (-3A+2B).(-3A+2B) = 9|A|^2+4|B|^2-12|A||B|cos60° = 9+4-6 = 7
|b|= √7
(2)
a.b
=(2A+B).(-3A+2B)
=-6|A|^2+2|B|^2 +|A||B|cos60°
= -6 +2 +1/2
=-7/2
(3)
a.b =|a||b|cosθ
-7/2 = 7cosθ
cosθ = -1/2
θ = 120°