If `D` is the mid-point of the side `B C` of a triangle `A B C ,` prove that ` vec A B+ vec A C=2 vec A Ddot`

Explanation

To prove that \( \vec{AB} + \vec{AC} = 2 \vec{AD} \), where \( D \) is the midpoint of side \( BC \) in triangle \( ABC \), we can follow these steps:

### Step 1: Set Up the Vectors
Let \( \vec{A}, \vec{B}, \vec{C} \) be the position vectors of points \( A, B, C \) respectively. Since \( D \) is the midpoint of \( BC \), we can express the position vector of \( D \) as:
\[ \vec{D} = \frac{\vec{B} + \vec{C}}{2} \]

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