已知向量a的绝对值为4,向量b的绝对值为3,(2a-3b)*(2a+b)=61

1
4a^2-6ab+2ab-3b^2=61
64-4ab-27=61
ab=-6
cosθ=-6/(4*3)=-1/2
θ=π-π/3=2π/3
2
(a+b)^2=a^2+2ab+b^2=16+2(-6)+9=13
︱a+b︱=√13
(a-b)^2=a^2-2ab+b^2=16-2(-6)+9=37
︱a-b︱=√37