Return the cross product of two (arrays of) vectors in Python

The cross product of two vectors produces a third vector perpendicular to both input vectors. In Python, we use numpy.cross() to compute the cross product of two (arrays of) vectors.

Syntax

numpy.cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)

Parameters

The numpy.cross() method accepts the following parameters:

• a - Components of the first vector(s)
• b - Components of the second vector(s)
• axisa - Axis of a that defines the vector(s). Default is the last axis
• axisb - Axis of b that defines the vector(s). Default is the last axis
• axisc - Axis of c containing the cross product vector(s). Default is the last axis
• axis - If defined, overrides axisa, axisb and axisc

Basic Cross Product Example

Let's compute the cross product of two 3D vectors ?

import numpy as np

# Creating two vectors
arr1 = [13, 11, 19]
arr2 = [19, 10, 8]

# Display the vectors
print("Vector 1:", arr1)
print("Vector 2:", arr2)

# Compute the cross product
result = np.cross(arr1, arr2)
print("Cross Product:", result)

Vector 1: [13, 11, 19]
Vector 2: [19, 10, 8]
Cross Product: [-102  257  -79]

Cross Product of 2D Vectors

For 2D vectors, the cross product returns a scalar value ?

import numpy as np

# 2D vectors
vec1 = [3, 4]
vec2 = [2, 5]

# Cross product of 2D vectors returns a scalar
result = np.cross(vec1, vec2)
print("2D Cross Product:", result)
print("Type:", type(result))

2D Cross Product: 7
Type: <class 'numpy.int64'>

Cross Product of Multiple Vector Pairs

You can compute cross products of multiple vector pairs simultaneously ?

import numpy as np

# Multiple 3D vectors
vectors_a = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
vectors_b = np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]])

# Cross product of multiple vector pairs
result = np.cross(vectors_a, vectors_b)
print("Multiple Cross Products:")
print(result)

Multiple Cross Products:
[[ 0  0  1]
 [ 1  0  0]
 [ 0  1  0]]

Key Properties

Conclusion

Use numpy.cross() to compute cross products of vectors in Python. For 3D vectors, it returns a perpendicular vector, while for 2D vectors, it returns a scalar representing the z-component magnitude.