If S is the mid-point of side QR of a `DeltaPQR`, then prove that `PQ+PR=2PS`.

Explanation

To prove that \( PQ + PR = 2PS \) given that \( S \) is the midpoint of side \( QR \) of triangle \( PQR \), we can use vector algebra. Here’s a step-by-step solution:

### Step 1: Define the position vectors
Let:
- \( \vec{P} \) be the position vector of point \( P \)
- \( \vec{Q} \) be the position vector of point \( Q \)
- \( \vec{R} \) be the position vector of point \( R \)
- Since \( S \) is the midpoint of \( QR \), we can express the position vector of \( S \) as:
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