The position vectors of points P, Q and R with respect to the origin are \((4i - 5j), (i + 3j)\) and \((-5i + 2j)\) respectively. If PQRM is a parallelogram...

The position vectors of points P, Q and R with respect to the origin are \((4i - 5j), (i + 3j)\) and \((-5i + 2j)\) respectively. If PQRM is a parallelogram, find:

(a) the position vector of M ;

(b) \(|\overrightarrow{PM}|\) and \(|\overrightarrow{PQ}|\) ;

(c) the acute angle between \(\overrightarrow{PM}\) and \(\overrightarrow{PQ}\), correct to 1 decimal place ;

(d) the area of PQRM.