# Cross Product – NumPy

Contents

## NumPy – Cross Product of Arrays

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.

## Examples

### 1. Cross product of vectors in 2D plane

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 Code Copy

Output

``11``

Mathematical Proof

``````cross(A,B) = 2*7 - 3*1
= 11``````

Consider that vectors [2,3] and [1,7] are in [X,Y] plane. Then the cross product  is in the axis perpendicular to [X,Y], say Z with magnitude 11.

### 2. Cross product of vectors in 3D plane

In this example, we shall take two NumPy Arrays, each of length 3 (representing a point in 3D space), 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 Code Copy

Output

``[20 -4 -3]``

Mathematical Proof

``````cross(A,B) = [(7*8-9*4), -(2*8-4*3), (2*9-7*3)]
= [20, -4, -3]``````

Output vector [20, -4, -3] is perpendicular to the plane formed by the input vectors [2, 7, 4], [3, 9, 8].

## Summary

In this NumPy Tutorial, we learned how to find cross product of two vectors using numpy.cross() function, with the help of well detailed example programs.

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