What is the cross product of two vectors?

Let’s say a and b are two three-dimensional vectors, i.e. both the vectors have 3 components. The cross product of these two vectors is defined as:

Here, c is another vector of the same dimension that is perpendicular to both a and b. So, we can also say,

Here, Θ is the angle between a and b. And ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.

How to calculate the cross product of two vectors using Python NumPy?

We can use the following Python code to compute the cross product of two three-dimensional vectors.

import numpy

a = numpy.array([1, 2, 3])
b = numpy.array([4, 5, 6])

c = numpy.cross(a, b)

print("a: \n", a)
print("b: \n", b)
print("The cross product of a and b: \n", c)

Here, a and b are two row vectors with three elements in each. We are using the numpy.cross() function to compute the cross product of a and b.

The output of the mentioned program will be:

a: 
 [1 2 3]
b: 
 [4 5 6]
The cross product of a and b: 
 [-3  6 -3]