Calculate the magnetic vector potential due to an infinite straight current carrying wire at a point located at distance r along a direction perpendicular to the wire. The current I in the wire is flowing in the x-direction.

The magnetic vector potential A due to a current-carrying wire is related to the current distribution through the equation:

\[
\mathbf{A}(\mathbf{r}) = \frac{\mu_0}{4\pi} \int \frac{I \, d\ell \, \hat{\mathbf{r'}}}{|\mathbf{r} - \mathbf{r'}|}
\]

where:
- \(\mu_0\) is the permeability of free space,
- \(I\) is the current in the wire,
- \(d\ell\) is an infinitesimal length element along the wire,
- \(\hat{\mathbf{r'}}\) is the unit vector along the direction ______ ______ ___ ____ ___ _________ __________ ____ __________ _____.
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