The position vector of a particle is given by `vec(r ) = k cos omega hat(i) + k sin omega hat(j) = x hat(i) + yhat(j)`, where `k` and `omega` are constants and `t` time. Find the angle between the position vector and the velocity vector. Also determine the trajectory of the particle.

Explanation

To solve the problem, we need to find the angle between the position vector and the velocity vector of a particle whose position vector is given by:

\[ \vec{r} = k \cos(\omega t) \hat{i} + k \sin(\omega t) \hat{j} \]

### Step 1: Identify the Position Vector
The position vector is already given as:
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