8 The points \(A ( 3,2,1 ) , B ( 5,4 , - 3 ) , C ( 3,17 , - 4 )\) and \(D ( 1,6,3 )\) form a quadrilateral \(A B C D\).
- Show that \(A B = A D\).
- Find a vector equation of the line through \(A\) and the mid-point of \(B D\).
- Show that \(C\) lies on the line found in part (ii).
- What type of quadrilateral is \(A B C D\) ?