use Python coding to answer question:

Consider the pyramid in 3d space with vertices ~v1 = (1, 1, 0), ~v2 = (1, 1, 0), ~v3 = (1, 1, 0), ~v4 = (1, 1, 0), ~v5 = (0, 0, 2).

i) Build a 3 5 matrix that has these vertices as its columns.

ii) Using matplotlib.pyplot, plot these 5 vertices as a 3-d scatter plot.

iii) Plot the lines connecting these 5 vertices, to draw the pyramid in a 3d plot. You should draw 8 lines total.

iv) Calculate all of the angles in the faces of this pyramid.