`vec(AC) and vec(BD)` are the diagonals of a parallelogram ABCD. Prove that
(i)`vec(AC) + vec(BD) - 2 vec(BC)`
(ii) `vec(AC) - vec(BD) - 2vec(AB)`

Explanation

To prove the statements regarding the diagonals of the parallelogram ABCD, we will use vector addition and properties of parallelograms.

### Given:
- \( \vec{AC} \) and \( \vec{BD} \) are the diagonals of parallelogram ABCD.
- Points A, B, C, and D are the vertices of the parallelogram.

### Step 1: Express the diagonals in terms of vectors
1. **Vector \( \vec{AC} \)**:
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