Contents
Numpy Cross Product
Cross product of two vectors yield a vector that is perpendicular to the plane formed by the input vectors and its magnitude is proportional to the area spanned by the parallelogram formed by these input vectors.
In this tutorial, we shall learn how to compute cross product using Numpy cross() function.
Example 1: Cross Product of Numpy Arrays
In this example, we shall take two points in XY plane as Numpy Arrays and find their cross product.
Python Program
import numpy as np
#initialize arrays
A = np.array([2, 3])
B = np.array([1, 7])
#compute cross product
output = np.cross(A, B)
print(output)
Run Output
11
Run Mathematical Proof
cross(A,B) = 2*7 - 3*1
= 11
Run Consider that vectors [2,3] and [1,7] are in [X,Y] plane. Then the cross product [11] is in the axis perpendicular to [X,Y], say Z with magnitude 11.
Example 2: Cross Product of Numpy Arrays in 3D
In this example, we shall take two 2×2 Numpy Arrays and find their cross product.
Python Program
import numpy as np
#initialize arrays
A = np.array([2, 7, 4])
B = np.array([3, 9, 8])
#compute cross product
output = np.cross(A, B)
print(output)
Run Output
[20 -4 -3]
Run Mathematical Proof
cross(A,B) = [(7*8-9*4), -(2*8-4*3), (2*9-7*3)]
= [20, -4, -3]
Run Output vector [20, -4, -3] is perpendicular to the plane formed by the input vectors [2, 7, 4], [3, 9, 8].
Summary
In this tutorial of Python Examples, we learned how to find cross product of two vectors using Numpy cross() function, with the help of well detailed example programs.