A particle moves in a plane such that its coordinates changes with time as `x = at` and `y = bt`, where a and b are constants. Find the position vector of the particle and its direction at any time t.

Explanation

To solve the problem step by step, we will derive the position vector of the particle and determine its direction at any time \( t \).

### Step 1: Define the coordinates of the particle
The coordinates of the particle are given as:
- \( x = at \)
- \( y = bt \)

where \( a \) and \( b \) are constants.
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