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

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

Therefore,

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