`A B C D` is a parallelogram. If `La n dM` are the mid-points of `B Ca n dD C` respectively, then express ` vec A La n d vec A M` in terms of ` vec A Ba n d vec A D` . Also, prove that ` vec A L+ vec A M=3/2 vec A Cdot`

Explanation

To solve the problem, we need to express the vectors \( \vec{A}L \) and \( \vec{A}M \) in terms of \( \vec{A}B \) and \( \vec{A}D \), and then prove that \( \vec{A}L + \vec{A}M = \frac{3}{2} \vec{A}C \).

### Step 1: Express \( \vec{A}L \)

1. **Identify the midpoint \( L \)**: Since \( L \) is the midpoint of \( BC \), we can express \( \vec{L} \) as:
\[ \vec{L} = \frac{\vec{B} + \vec{C}}{2} \]
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