`A B C` is a triangle. `D` is a point on `A B` such that `A D=1/4A B` and `E` is a point on `A C` such that `A E=1/4A Cdot` Prove that `D E=1/4B Cdot`

Explanation

To prove that \( DE = \frac{1}{4} BC \) given that \( AD = \frac{1}{4} AB \) and \( AE = \frac{1}{4} AC \), we can follow these steps:

### Step 1: Define Points and Ratios
Let \( A, B, C \) be the vertices of triangle \( ABC \). We know:
- \( D \) is a point on \( AB \) such that \( AD = \frac{1}{4} AB \).
- \( E \) is a point on \( AC \) such that \( AE = \frac{1}{4} AC \).

### Step 2: Express Lengths in Terms of Vectors
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