How to compute the cross product of two given vectors using NumPy?

How to compute the cross product of two given vectors using NumPy?

To compute the cross product of two vectors in NumPy, you can use the numpy.cross function. The function takes two array-like objects representing vectors and returns their cross product.

Here's an example of how you can use numpy.cross:

import numpy as np

# Define two vectors
vector_a = np.array([1, 2, 3])
vector_b = np.array([4, 5, 6])

# Compute the cross product
cross_product = np.cross(vector_a, vector_b)

print(cross_product)  # Output will be [-3  6 -3]

The result is a new vector that is perpendicular to both vector_a and vector_b, assuming they are three-dimensional vectors.

For two-dimensional vectors, you can still use numpy.cross, but you should represent your 2D vectors in 3D space with a zero z-component:

# Define two 2D vectors, extended to 3D with a zero z-component
vector_a_2d = np.array([1, 2, 0])
vector_b_2d = np.array([4, 5, 0])

# Compute the cross product
cross_product_2d = np.cross(vector_a_2d, vector_b_2d)

print(cross_product_2d)  # Output will be [0 0 -3]

The result will be a 3D vector where only the z-component is non-zero, reflecting the perpendicular vector in the z-direction. The magnitude of this vector is equal to the area of the parallelogram formed by the two 2D vectors.

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