Why does the Biot-Savart law use both r and r-hat?

[Astrum]

I'm not sure I get how:$$\frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\vec{r})}{r^{3}}$$ = $$\frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\hat{r})}{r^{2}}$$

the r is a displacement vector in the first, and in the second it's a unit vector, but why is this so?

 

[HomogenousCow]

The second expression is correct, the first one is not.

 

[Astrum]

Sorry, meant to put a cubed there. Fixed

 

[qbert]

There's nothing really to get: $\widehat{r} = \frac{ \vec{r} }{r}$.

 

[Astrum]

I see,another dumb question I asked, sorry for wasting your time...