How can I make a 3D line plot?

I guess, you want to plot 4 lines. Then you can try

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

for i in range(4):
    ax.plot([VecStart_x[i], VecEnd_x[i]], [VecStart_y[i],VecEnd_y[i]],zs=[VecStart_z[i],VecEnd_z[i]])

As Nicolas has suggested, do have a look at the matplotlib gallery.