13. The position vectors of the points \(A\) and \(B\), relative to a fixed origin \(O\), are given by
$$\mathbf { a } = 4 \mathbf { i } + 7 \mathbf { j } , \quad \mathbf { b } = \mathbf { i } + 3 \mathbf { j }$$
respectively.
- Find the vector \(\mathbf { A B }\).
- Determine the distance between the points \(A\) and \(B\).
- The position vector of the point \(C\) is given by \(\mathbf { c } = - 2 \mathbf { i } + 5 \mathbf { j }\). The point \(D\) is such that the distance between \(C\) and \(D\) is equal to the distance between \(A\) and \(B\), and \(C D\) is parallel to \(A B\). Find the possible position vectors of the point \(D\).