N2018 P2 Q3

An oblique pyramid has a plane base \(ABCD\) in the shape of a parallelogram. The coordinates of \(A\), \(B\) and \(C\) are \((5,-4,1)\), \((5,4,0)\) and \((-5,4,2)\) respectively. The apex of the pyramid is at \(E(0,0,10)\) (see diagram).

1. Find the coordinates of \(D\).[1]
2. Find the cartesian equation of face \(BCE\).[3]
3. Find the angle between face \(BCE\) and the base of the pyramid.[3]
4. Find the shortest distance from the midpoint of edge \(AD\) to face \(BCE\).[5]