Express vector $\mathbf{G}=\rho \sin \phi \mathbf{a}_{\rho}-\rho \cos \phi \mathbf{a}_{\phi}+\rho \mathbf{a}_{z}$ in rectangular coordinates.

In this task we need to find vector:

$$\begin{aligned} \bold{G}=\rho\sin(\phi)\bold{a_{\rho}}-\rho\cos(\phi)\bold{a_{\phi}}+\rho\bold{a_{z}} \end{aligned}$$

in rectangular coordinates which is another name for Cartesian coordinates $(x,y,z)$. We can clearly see that vector $\bold{G}$ is vector in cylindrical coordinates.