We have a wire with cross-sectional area $A$, length $L$ and current $I$.
If the wire is in a magnetic field $\vec B$, the magnetic force on each charge is $\vec F =q\vec v_d \times \vec B$.
$\vec v_d$ is the drift velocity or average velocity
The number of charges in the wire segment is the number $n$ per unit volume, multiplied by the volume $AL$.
Thus the total force in the wire segments is $$(1)\: \:\vec F =(q\vec v_d \times \vec B)nAL$$
We know that the current in the wire is $(2)$ $I=nqv_d A$
Combining (2) and (1) the force can be written as $(3)$ $\vec F=I\vec L \times \vec B$
This is a paragraph from my textbook.
I know that the cross product has the property $(rA \times B)=(A \times rB) = r(A \times B)$
What I don't understand is why $\vec v_d$, that is a vector in (1) becomes a scalar in (3) as a part of $I$. And why, on the other hand, $L$ that is an scalar in (1) becomes a vector in (3). What property allows you to do that?