A sheet of metal in the shape of a parallelogram ABCD (labelled so that the diagonals are AC and BD) is hanging from the ceiling. Three vertices are located at A = (1, 2, 6), B = (3, 3, 4), C = (2, 3, 3) (all in metres).

a) Find the vectors BA and BC.

b) Find the location of the vertex D.

c) Show that the parallelogram is in fact a rectangle.

d) Find the area of the metal sheet.

e) Calculate the exact angle that the edge BA makes with the vertical z-axis.