Assuming we have vector A with elements (A_{1}, A_{2}, A_{3}) and vector B with elements (B_{1}, B_{2}, B_{3}), we can calculate the cross product of these two vectors as:

**Cross Product** = [(A_{2}*B_{3}) – (A_{3}*B_{2}), (A_{3}*B_{1}) – (A_{1}*B_{3}), (A_{1}*B_{2}) – (A_{2}*B_{1})]

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 = [(A
_{2}*B_{3}) – (A_{3}*B_{2}), (A_{3}*B_{1}) – (A_{1}*B_{3}), (A_{1}*B_{2}) – (A_{2}*B_{1})] - 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 cross() 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.

**Additional Resources**

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

How to Calculate Dot Product Using NumPy

How to Normalize a NumPy Matrix

How to Add Row to Matrix in NumPy