A particle move in `x-y` plane such that its position vector varies with time as `vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j`. Find the equation of the trajectory of the particle.

Explanation

To find the equation of the trajectory of the particle given its position vector, we can follow these steps:

### Step 1: Write down the position vector
The position vector of the particle is given as:
\[ \vec{r} = 2 \sin(3t) \hat{i} + 2(1 - \cos(3t)) \hat{j} \]
This can be rewritten in terms of its components:
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