The angle between vecA→A and vecB→B is given by the dot product definition.
vecA.vecB=∥vecA∥*∥vecB∥costheta→A.→B=∥→A∥⋅∥→B∥cosθ
Where thetaθ is the angle between vecA→A and vecB→B
The dot product is
vecA.vecB=〈-3,2,0〉.〈6,-9,8〉=-18-18+0=-36→A.→B=⟨−3,2,0⟩.⟨6,−9,8⟩=−18−18+0=−36
The modulus of vecA→A= ∥〈-3,2,0〉∥=sqrt(9+4+0)=sqrt13∥∥⟨−3,2,0⟩∥=√9+4+0=√13
The modulus of vecB→B= ∥〈6,-9,8〉∥=sqrt(36+81+64)=sqrt181∥∥⟨6,−9,8⟩∥=√36+81+64=√181
So,
costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-36/(sqrt13*sqrt181)=-0.742cosθ=→A.→B∥∥∥→A∥⋅∥→B∥∥∥=−36√13⋅√181=−0.742
theta=137.9θ=137.9º
