How to calculate a Cross Product in Python

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Assuming we have vector A with elements (A₁, A₂, A₃) and vector B with elements (B₁, B₂, B₃), we can calculate the cross product of these two vectors as:

Cross Product = [(A₂*B₃) – (A₃*B₂), (A₃*B₁) – (A₁*B₃), (A₁*B₂) – (A₂*B₁)]

For example, suppose we have the following vectors:

• Vector A: (1, 2, 3)
• Vector B: (4, 5, 6)

We could calculate the cross product of these vectors as:

• Cross Product = [(A₂*B₃) – (A₃*B₂), (A₃*B₁) – (A₁*B₃), (A₁*B₂) – (A₂*B₁)]
• Cross Product = [(2*6) – (3*5), (3*4) – (1*6), (1*5) – (2*4)]
• Cross Product = (-3, 6, -3)

You can use one of the following two methods to calculate the cross product of two vectors in Python:

Method 1: Use cross() function from NumPy

import numpy as np
  
#calculate cross product of vectors A and B
np.cross(A, B)

Method 2: Define your own function

#define function to calculate cross product 
def cross_prod(a, b):
    result = [a[1]*b[2] - a[2]*b[1],
            a[2]*b[0] - a[0]*b[2],
            a[0]*b[1] - a[1]*b[0]]

    return result

#calculate cross product
cross_prod(A, B)

The following examples show how to use each method in practice.

Example 1: Use cross() function from NumPy

The following code shows how to use the function from NumPy to calculate the cross product between two vectors:

import numpy as np

#define vectors
A = np.array([1, 2, 3])
B = np.array([4, 5, 6])
  
#calculate cross product of vectors A and B
np.cross(A, B)

[-3, 6, -3]

The cross product turns out to be (-3, 6, -3).

This matches the cross product that we calculated earlier by hand.

Example 2: Define your own function

The following code shows how to define your own function to calculate the cross product between two vectors:

#define function to calculate cross product 
def cross_prod(a, b):
    result = [a[1]*b[2] - a[2]*b[1],
            a[2]*b[0] - a[0]*b[2],
            a[0]*b[1] - a[1]*b[0]]

    return result

#define vectors
A = np.array([1, 2, 3])
B = np.array([4, 5, 6])

#calculate cross product
cross_prod(A, B)

[-3, 6, -3]

The cross product turns out to be (-3, 6, -3).

This matches the cross product that we calculated in the previous example.

The following tutorials explain how to perform other common tasks in Python: