Question

Why do axial vectors dont produce motion eg when a bullock cart moves why the wheel does not come out due to axial vector pointing outwards according to right hand rule

Answer 1

Indeed, when the wheels move forward and then have momentum $\textbf{p}$, they achieve the angular momentum:

$$\textbf{L}=\textbf{r}\times\textbf{p}.$$

But what does the angular momentum represent? Is it a force? Let's see.

According to the expression, it's measured in units of distance times units of momentum:

$$\text{kg}\cdot\text{m}^2/\text{s},$$

it is not Newton and thus it's not a force. The angular momentum just measures how much inertia a rotating body has. What can make the wheels come out, however, is a force. Forces can produce motion as you correctly mentioned, but what is produced in the described situation is not a force.