curriculum/challenges/english/blocks/learn-special-methods-by-building-a-vector-space/6601a8fb2e993b55912f9e9f.md
The cross product between two 3D vectors \( \mathbf{a} \) and \( \mathbf{b} \) can be computed as it follows:
\[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} a_yb_z - a_zb_y \\ a_zb_x - a_xb_z \\ a_xb_y - a_yb_x \end{pmatrix} \]
Where the resulting vector is represented as a column vector.
Implement the formula above to compute the cross product between two 3-dimensional vectors and return the resulting vector from the cross() method.
The cross() method should return a new R3Vector instance resulting from the cross product computation.
({ test: () => assert(runPython(`
v1 = R3Vector(x=2, y=3, z=1)
v2 = R3Vector(x=0.5, y=1.25, z=2)
v1.cross(v2) == R3Vector(x=4.75, y=-3.5, z=1.0) and v2.cross(v1) == R3Vector(x=-4.75, y=3.5, z=-1.0) and v1.cross(v1) == R3Vector(x=0, y=0, z=0)
`)) })
class R2Vector:
def __init__(self, *, x, y):
self.x = x
self.y = y
def norm(self):
return sum(val**2 for val in vars(self).values())**0.5
def __str__(self):
return str(tuple(getattr(self, i) for i in vars(self)))
def __repr__(self):
arg_list = [f'{key}={val}' for key, val in vars(self).items()]
args = ', '.join(arg_list)
return f'{self.__class__.__name__}({args})'
def __add__(self, other):
if type(self) != type(other):
return NotImplemented
kwargs = {i: getattr(self, i) + getattr(other, i) for i in vars(self)}
return self.__class__(**kwargs)
def __sub__(self, other):
if type(self) != type(other):
return NotImplemented
kwargs = {i: getattr(self, i) - getattr(other, i) for i in vars(self)}
return self.__class__(**kwargs)
def __mul__(self, other):
if type(other) in (int, float):
kwargs = {i: getattr(self, i) * other for i in vars(self)}
return self.__class__(**kwargs)
elif type(self) == type(other):
args = [getattr(self, i) * getattr(other, i) for i in vars(self)]
return sum(args)
return NotImplemented
def __eq__(self, other):
if type(self) != type(other):
return NotImplemented
return all(getattr(self, i) == getattr(other, i) for i in vars(self))
def __ne__(self, other):
return not self == other
def __lt__(self, other):
if type(self) != type(other):
return NotImplemented
return self.norm() < other.norm()
def __gt__(self, other):
if type(self) != type(other):
return NotImplemented
return self.norm() > other.norm()
def __le__(self, other):
return not self > other
def __ge__(self, other):
return not self < other
--fcc-editable-region--
class R3Vector(R2Vector):
def __init__(self, *, x, y, z):
super().__init__(x=x, y=y)
self.z = z
def cross(self, other):
if type(self) != type(other):
return NotImplemented
kwargs = {}
--fcc-editable-region--
v1 = R2Vector(x=2, y=3)
v2 = R2Vector(x=0.5, y=1.25)
print(f'v1 = {v1}')
print(f'v2 = {v2}')
v3 = v1 + v2
print(f'v1 + v2 = {v3}')
v4 = v1 - v2
print(f'v1 - v2 = {v4}')
v5 = v1 * v2
print(f'v1 * v2 = {v5}')