Determine velocity of track curve The track curve of a particle is described with respect to an inertial cartesian coordinate system with the position vector with constants $a$, $b$, $\omega
$ and time variable $t$.
$\vec{r}=acos(\omega t) \vec{e_{x} }+bsin(\omega t) \vec{e_{y} } 
 $
i) With which dimensions are the constants $a$, $b$ and $\omega
$ associated? Which form has the track curve (sketch)?
ii) Calculate velocity of the particle (vector) and their magnitude?
iii) Give the unit tangenten vector of the track curve.
What I think:
a) I dont know this part, not even sure what question really means.
b) I think i should use this formula $\vec{v}=\frac{d\vec{r}}{dt} $
c) I should only divide vector with magnitude from b): $T=\frac{\vec{r} ' }{| \vec{r}'  | }  $
Can someone help me with a) and tell me are b) and c) good?
 A: You are abolutely right for b) and c), these are definitions of velocity and tangent vector
Regarding a), nothing of the context is given. The dimension can mean "unit" in physics (I have seen it). As for the form, I hope more is given to you.
Following comment : With your formula it becomes clearer. $a$ and $b$ are indeed lengths, $\omega$ an angle per second (which means only $s^{-1}$) and your particle is moving on an ellipse. 
A: To address part (i), the dimensions of $a$ and $b$ are length. These parameters denote the major and minor axes of the elliptical track. To draw such a track, the track would be elliptical, like an oval, and the "long edge" could be $a$, say, and the "short edge" could be $b$. Note that if $a = b$, then the track is circular since the position vector parametrizes a circle of radius $r = a = b$. In general, $a\ne b,$ and the track must be drawn to show that radius is not uniform and is instead scaled by a factor $a$ in the $x$-direction and $b$ in the $y$-direction. The parameter $t$ has dimensions of time. The parameter $\omega$ also has dimensions of inverse time, not only because it is an angular speed but also because the argument of the trigonometric functions must be dimensionless.
