2023 SJI P2 Q3

Consider an isosceles triangle \(PQR\) with coordinates \(P(3,7,5)\), \(Q(1,m,-2)\) and \(R(2,2,3)\), where \(m\) is a non-zero constant. It is given that \(PR=QR\).

1. Find the value of \(m\).[4]
2. Find the midpoint of \(PQ\).[2]
3. Hence find the value of \(\cos\angle RPQ\).[3]