Answer & Explanation
Let corresponding coutesian cordinates are,
Relation between coutesian cordinates and sherical coordinates are
Distance between paints
The expression of the distance between two vectors in spherical coordinates provided in the other response is usually expressed in a more compact form that is not only easier to remember but is also ideal for capitalizing on certain symmetries when solving problems.
This form makes it fairly transparent how azimuthal symmetry allows you to automatically eliminate some of the angular dependencies in certain integration problems
Another advantage of this form is that you now have at least two variables, namely
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