Let AB be a vector in two dimensional plane with the magnitude 4 units and making an angle of `30^(@)` with X-axis and lying in the first quadrant. Find the components of AB along the two axes off coordinates. Hence, represent AB in terms of unit vectors `hati and hatj`.

Explanation

To solve the problem, we need to find the components of the vector \( \vec{AB} \) along the x-axis and y-axis, and then express it in terms of the unit vectors \( \hat{i} \) and \( \hat{j} \).

### Step 1: Identify the given information
- Magnitude of vector \( \vec{AB} = 4 \) units
- Angle \( \theta = 30^\circ \) with the x-axis
- The vector lies in the first quadrant.

### Step 2: Calculate the x-component of the vector
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