Vector fields A and B are given as following. \mathbf{A}=(z-\sin (\emptyset)) \mathbf{a}_{\boldsymbol{\rho}}+(2 \rho+2 \cos (\emptyset)) \boldsymbol{a}_{\phi}-5 \rho z \mathbf{a}_{\mathbf{z}} \mathbf{B}=\rho \cos (\emptyset) \mathbf{a}_{\boldsymbol{\rho}}+\sin (\emptyset) \boldsymbol{a}_{\boldsymbol{\phi}}+4 \mathbf{a}_{\mathbf{z}} \text { ots] Calculate

the angle between } \mathbf{A} \text { and } \mathbf{B} \text { at } P\left(1, \frac{\pi}{4},-2\right) \text {. } \text { s] Derive the unit vector which is perpendicular to both } \mathbf{A} \text { and } \mathbf{B} \text { at } P\left(5, \frac{2 \pi}{3}, 0\right) \text {. }