The correct Biot-Savart law in vector form is

1
\(d\vec B = \frac{{{\mu _0}}}{{4\pi }}\frac{{I\left( {d\vec l \times \vec r} \right)}}{{{r^2}}}\)
2
\(d\vec B = \frac{{{\mu _0}}}{{4\pi }}\frac{{I\left( {d\vec l \times \vec r} \right)}}{{{r^3}}}\)
3
\(d\vec B = \frac{{{\mu _0}}}{{4\pi }}\frac{{Id\vec l}}{{{r^2}}}\)
4
\(d\vec B = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{Id\vec l}}{{{r^3}}}\)

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