Cross product of two vectors in Python

Question

How can I calculate the cross product of two vectors without the use of programming libraries?

E.g given vectors a = (1, 2, 3) and b = (4, 5, 6)

Answer 1

are you asking about the formula for the cross product? Or how to do indexing and lists in python?

The basic idea is that you access the elements of a and b as a[0], a[1], a[2], etc. (for x, y, z) and that you create a new list with [element_0, element_1, ...]. We can also wrap it in a function.

On the vector side, the cross product is the antisymmetric product of the elements, which also has a nice geometrical interpretation.

Anyway, it would be better to give you hints and let you figure it out, but that's not really the SO way, so...

def cross(a, b):
    c = [a[1]*b[2] - a[2]*b[1],
         a[2]*b[0] - a[0]*b[2],
         a[0]*b[1] - a[1]*b[0]]

    return c

Answer 2

import numpy as np
a = np.array([1,0,0])  
b = np.array([0,1,0])  
#print the result    
print(np.cross(a,b))

Answer 3

If you want to implement the cross product yourself you may see http://en.wikipedia.org/wiki/Vector_cross_product or a math/physics book. Shortly (a1, a2, a3) X (b1, b2, b3) = (a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)