If ABCDEF is a regular hexagon, prove that `AD+EB+FC=4AB`.

Explanation

To prove that \( \vec{AD} + \vec{EB} + \vec{FC} = 4\vec{AB} \) for a regular hexagon \( ABCDEF \), we can follow these steps:

### Step 1: Understand the Geometry of the Hexagon
A regular hexagon can be inscribed in a circle, and all its sides are equal. Let the length of each side be \( AB = a \). The vertices of the hexagon can be represented in a coordinate system.

### Step 2: Assign Coordinates to the Vertices
We can assign coordinates to the vertices of the hexagon as follows:
- \( A(1, 0) \)
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