Products

 Vectors, it will be recalled, have both length and direction. One can multiply one with the other

to find magnitude with the dot product. 

The result is a scalar. We are still in a 2D space and need the cos value to correct the

outcome as a function of orientation.

The cross product is something else: we are still multiplying the absolute length values,

but correcting with the sine function, and + or - orientation. The result here is a new

vector, but in a 3D space.

                                                                       

                                                                  

                                                                                 

import numpy as np

# Define the two vectors
vector1 = np.array([2, 3])
vector2 = np.array([-4, 5])

# Calculate the cross product
cross_product = np.cross(vector1, vector2)

# Print the result
print(cross_product)

import matplotlib.pyplot as plt
import numpy as np

# Define the vector
#vector = np.array([1, 2, 3])
vector = ([2, 3, 0])
vector1 = ([-4, 5, 0])
vector2 = ([0, 0, cross_product])


# Create a figure and axis object
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Draw the vector using quiver()
ax.quiver(0, 0, 0, vector[0], vector[1], vector[2], color='orange')
ax.quiver(0, 0, 0, vector1[0], vector1[1], vector1[2], color='red')
ax.quiver(0, 0, 0, vector2[0], vector2[1], vector2[2], color='black')

# Set the x, y, and z limits of the plot
ax.set_xlim([-5, 5])
ax.set_ylim([-5, 5])
ax.set_zlim([-5, 5])

# Add a grid to the plot
ax.grid(True)

# Show the plot
plt.show()

                                                                                  

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