Step 1

Given: \(a)\overrightarrow{A}(x,y,z)=\overrightarrow{e}_{x}\)

To express it in other two coordinate systems:

ie., in terms of cartesian, cylindrical and spherical coordinates

Step 2

Given: \(a)\overrightarrow{A}(x,y,z)=\overrightarrow{e}_{x}\)

spherical coordinates can be expressed as

\((r, \theta, \phi)=(\sqrt{x^{2}+y^{2}+z^{2}}, \tan^{-1} (\frac{y}{x}), \cos^{-1}(\frac{z}{\sqrt{x^{2}+y^{2}+z^{2}}}))\)

Therefore,

\(\displaystyle{\left({r},\theta,\phi\right)}={\left({1},{0},{\frac{{\pi}}{{{2}}}}\right)}\)