import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# algebraic 2-dimensional vector representation
v1 = np.array([ 1, 2])

# algebraic 3-dimensional vector representation
v2 = np.array([ 1,2,3])

# geometric representation of v1
plt.plot([0,v1[0]],[0,v1[1]])
plt.axis('equal')
plt.plot([-4, 4],[0, 0],'k--')
plt.plot([0, 0],[-4, 4],'k--')
plt.grid()
plt.axis((-4, 4, -4, 4))
plt.show()


# geometric representation of v2
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot([0, v2[0]],[0, v2[1]],[0, v2[2]])

# make the plot look nicer
plt.axis('equal')
ax.plot([0, 0],[0, 0],[-4, 4],'k--')
ax.plot([0, 0],[-4, 4],[0, 0],'k--')
ax.plot([-4, 4],[0, 0],[0, 0],'k--')
plt.show()