I have a vector of the form $P\hat{z}$ in the Cartesian system. I need to perform a dot product with another vector which is the spherical form. I figured it would be easier to convert $P\hat{z}$ into the spherical form and my immediate guess was the form would be $P\hat{r}$ with $\theta$ and $\phi$ zero meaning $\theta$ was "pointing" upwards or in the $z$ direction. As for $\phi$, any value should essentially give me the same thing.
This intuition appears to be clearly wrong. Deciding to use some of Mathematica's magic, I plugged in $(0,0,P)$ and attempted conversion from Cartesian to Spherical which threw the following error-
ArcTan::indet: Indeterminate expression ArcTan[0,0] encountered.
And the output was-
$\{\sqrt{P^2},\tan ^{-1}(P,0),\text{Indeterminate}\}$
which is what I originally thought of.
How do I perform a dot product with this when $\phi$ is indeterminate?
