# Independence of position and velocity vector [duplicate]

Hi I am a mathematics student with an interest in Physics. In our Physics elective our prof. said if $$\vec r$$ denotes the position vector then the velocity vector $$\vec v = \vec {\dot r}$$ is independent of $$\vec r$$. I don't understand what this means. Is it linear independence in the sense of linear algebra ? But in that case if $$\vec r (t) = t \hat i$$ then $$\vec r(t)$$ and $$\vec v(t) = \hat i$$ are always linearly dependent.

Kindly explain this concept to me.

## marked as duplicate by ACuriousMind♦Apr 14 at 18:34

• @IgnorantMathematician If you take the derivative of the position vector, you can see that there are terms with $r$. And then depending on the type of the problem, you could evaluate those parameters. It could depend on $r$ in the end ... or it would not. – KV18 Apr 14 at 18:40