If `A B C D` is quadrilateral and `Ea n dF` are the mid-points of `A Ca n dB D` respectively, prove that ` vec A B+ vec A D` +` vec C B` +` vec C D` =4 ` vec E Fdot`

Explanation

To prove that \( \vec{AB} + \vec{AD} + \vec{CB} + \vec{CD} = 4 \vec{EF} \), where \( E \) and \( F \) are the midpoints of \( AC \) and \( BD \) respectively, we can follow these steps:

### Step 1: Define the Position Vectors
Let the position vectors of points \( A, B, C, D \) be represented as \( \vec{A}, \vec{B}, \vec{C}, \vec{D} \) respectively.

### Step 2: Find the Position Vectors of Midpoints
Since \( E \) is the midpoint of \( AC \), we can express the position vector of \( E \) as:
\[
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