4 The points \(\mathrm { A } , \mathrm { B }\) and C are given by the position vectors \(\mathbf { a } = \binom { - 2 } { 1 } , \mathbf { b } = \binom { 0 } { 5 }\) and \(\mathbf { c } = \binom { 4 } { 3 }\). M is the midpoint of AC .
- Find the position vector of M .
- Find the vector \(\overrightarrow { B C }\).
- Find the position vector of the point D such that \(\overrightarrow { \mathrm { BC } } = \overrightarrow { \mathrm { AD } }\).
- Show that D lies on BM .