5 Points \(A , B , C\) and \(D\) have position vectors \(\mathbf { a } = \binom { 1 } { 2 } , \mathbf { b } = \binom { 3 } { 5 } , \mathbf { c } = \binom { 7 } { 4 }\) and \(\mathbf { d } = \binom { 4 } { k }\).
- Find the value of \(k\) for which \(D\) is the midpoint of \(A C\).
- Find the two values of \(k\) for which \(| \overrightarrow { A D } | = \sqrt { 13 }\).
- Find one value of \(k\) for which the four points form a trapezium.