Consider a spherical coordinate system. Let a point be represented by $(r, \theta, \phi)$, in that order. Now that the order of the coordinates is established, I can define unit vectors that form…

Read moreIn this post, I write the azimuthal unit vector $\vec{e}_{\phi}$ in terms of Cartesian coordinates. Here, $\phi$ is the azimuthal angle in the $x-y$ plane. As noted in this post, $\vec{e}_{\phi}$ points in the direction…

Read moreThis post introduced the following questions. What direction does $\vec{e}_{\phi}$ point? Modern convention dictates that $\vec{e}_{\phi}$ should point in the direction of increasing $\phi$, but what is the reason for this convention? If there are…

Read moreA coordinate system can be defined by three perpendicular unit vectors. If the coordinate system is Cartesian, which direction does the $+x$ axis point? To resolve this problem, I define an orientation–a coordinate system…

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