If `Da n dE` are the mid-points of sides `A Ba n dA C` of a triangle `A B C` respectively, show that ` vec B E+ vec D C=3/2 vec B Cdot`

Explanation

To solve the problem, we need to show that \( \vec{BE} + \vec{DC} = \frac{3}{2} \vec{BC} \).

### Step-by-Step Solution:

1. **Identify Points and Vectors:**
- Let \( A \), \( B \), and \( C \) be the vertices of triangle \( ABC \).
- Let \( D \) be the midpoint of side \( AB \), and \( E \) be the midpoint of side \( AC \).
- Therefore, we can express the position vectors of \( D \) and \( E \) as:
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