The correct Biot-Savart law in vector form is:
$\vec{dB} = \frac{\mu_0 I (d\vec{l} \times \vec{r})}{4\pi r^2}$
$\vec{dB} = \frac{\mu_0 I (d\vec{l} \times \vec{r})}{4\pi r^3}$
$\vec{dB} = \frac{\mu_0 I d\vec{l}}{4\pi r^2}$
$\vec{dB} = \frac{\mu_0 I d\vec{l}}{4\pi r^3}$
