Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in...

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
$(r,\theta ,\varphi )=(\sqrt{x^2+y^2+z^2},{\tan }^{-1}(\frac{y}{x}),{\cos }^{-1}(\frac{z}{\sqrt{x^2+y^2+z^2}}))$
Therefore,
${\displaystyle (r,\theta ,\varphi )=(1,0,\frac{\pi }{2})}$