# Cross Product in NumPy | Python

NumPy `cross()` function in Python is used to compute the cross-product of two given vector arrays. In other words. A cross product is a mathematical tool to get the perpendicular vector component of two vector coordinates. In this article, I will explain how to use` numpy.cross()` function and get the cross product of two arrays of vectors.

## 1. Quick Examples of Cross Product

If you are in a hurry, below are some quick examples of how to use NumPy cross product in Python.

``````
# Below are the quick examples

# Example 1: Use numpy.cross() function
arr = np.array([2, 4])
arr1 = np.array([1, 5])
arr2 = np.cross(arr, arr1)

# Example 2: cross product of a 2X3 array
arr = np.array([2,4,6])
arr1 = np.array([3,5,2])
arr2 = np.cross(arr, arr1)

# Example 3: One Vector 2D
arr = np.array([2,4])
arr1 = np.array([3,5,2])
arr2 = np.cross(arr, arr1)

# Example 4: Get cross product of numpy arrays in 2D
arr =  np.array([[2,4,6], [3,5,7]])
arr1 = np.array([[3,5,7], [2,4,6]])
arr2 = np.cross(arr, arr1)
``````

## 2. Syntax of NumPy cross()

Following is the syntax to create `cross()` function.

``````
# Syntax of numpy.cross()
numpy.cross(arr, arr1, axisa=- 1, axisb=- 1, axisc=- 1, axis=None)
``````

### 2.1 Parameters of NumPy cross()

Following are the parameters of the NumPy `cross()`.

• `arr` – This is an array_like component of the first vector(s).
• `arr1` – This is an array_like component of the second vector(s).
• `axisa` – This is the axis of arr that defines the vector(s). Its default value is the last axis.
• `axisb` – This is the Axis of arr1 that defines the vector(s). Its default value is the last axis.
• `axisc` – This is the axis of the third vector that contains the cross-product vector. Ignored if both input vectors have two dimensions, as the return is scalar.
• `axis `– If defined, the axis of the first, second and third that defines the vector(s) and cross products. It overrides axisa, axisb and axisc.

### 2.2 Return Value of cross()

It returns the cross product of two arrays of vectors.

## 3. Use numpy.cross() Function

Using two arrays, `arr= [2,4`], and `arr1= [1,5]` to cross vector product, we need to get the difference between the product of i1-j2 and i2-j1. The vector-product of two 2-Dimensional arrays will always be a single-dimensional integer. The final result is `(2*5)–(4*1) = 6.`

``````
import numpy as np

# creating input array
arr = np.array([2, 4])
arr1 = np.array([1, 5])

# Use numpy.cross() function to cross product of 2X2 matrix
arr2 = np.cross(arr, arr1)
print(arr2)

# Output
# 6
``````

Yields below output.

``````
# Mathematical Proof
cross(arr, arr1) = 2*5 - 4*1
= 6
``````

## 4. Cross Product of a 2X3 Matrix

To compute the cross product of two vectors, use the `numpy.cross()` function. it will return the cross product of two arrays of vectors. Let’s take an example,

``````
import numpy as np

# creating input array
arr = np.array([2,4,6])
arr1 = np.array([3,5,2])

# cross product of a 2X3 array
arr2 = np.cross(arr, arr1)
print(arr2)

# Output
# [-22  14  -2]
``````

Yields below output.

``````
# Mathematical Proof
cross(arr,arr1) = [(4*2-5*6), -(2*2-6*3), (2*5-4*3)]
= [-22, -14, -2]
``````

One vector with two dimensions.

``````
import numpy as np

# creating input array
arr = np.array([2,4])
arr1 = np.array([3,5,2])

# One Vector 2D
arr2 = np.cross(arr, arr1)
print(arr2)

# Output
# [ 8 -4 -2]
``````

## 5. Get Cross Product of NumPy Arrays in 2D

The `np.cross()` function is used to find out the cross product of two arrays. The `cross()` function takes arr and arr1 as arguments and returns the cross product of two arrays of vectors.

``````
import numpy as np

# creating an 2D input array
arr =  np.array([[2,4,6], [3,5,7]])
arr1 = np.array([[3,5,7], [2,4,6]])

# Get cross product of numpy arrays in 2D
arr2 = np.cross(arr, arr1)
print(arr2)
``````

The following calculation is shown a 2-D matrix cross product.

``````
# [[-2  4 -2]
# [ 2 -4  2]]
``````

## 6. Conclusion

In this article, I have explained how to use Python `numpy.cross()` function to perform cross product of two given vector arrays with examples.

Happy Learning!!