Cross product of two vectors in Python
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)
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
import numpy as np
a = np.array([1,0,0])
b = np.array([0,1,0])
#print the result
print(np.cross(a,b))
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)
for multiple dimensions, this might work;
def crossProd(a,b):
dimension = len(a)
c = []
for i in range(dimension):
c.append(0)
for j in range(dimension):
if j <> i:
for k in range(dimension):
if k <> i:
if k > j:
c[i] += a[j]*b[k]
elif k < j:
c[i] -= a[j]*b[k]
return c