Please prove above operator that in spherical polar coordinates.
Added by Alvaro J.
Step 1
In this coordinate system, a point in space is described by its distance from the origin (r), its polar angle (θ) measured from the positive z-axis, and its azimuthal angle (φ) measured from the positive x-axis in the xy-plane. Show more…
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Show that in spherical coordinates: (a) $\rho$ is the length of $x \mathbf{i}+y \mathbf{j}+z \mathbf{k}.$ (b) $\phi=\cos ^{-1}(\mathbf{v} \cdot \mathbf{k} /\|\mathbf{v}\|),$ where $\mathbf{v}=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}.$ (c) $\theta=\cos ^{-1}(\mathbf{u} \cdot \mathbf{i} /\|\mathbf{u}\|),$ where $\mathbf{u}=x \mathbf{i}+y \mathbf{j}.$
The Geometry of Euclidean Space
Cylindrical and Spherical Coordinates
Express in spherical polar coordinates: $$ x^{2}-y^{2} $$
Express in spherical polar coordinates: $$ \left(x^{2}+y^{2}\right) / z^{2} $$
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