import math

class Vector2d:
	def __init__(self, x, y):
		self.points = [x, y]
		
	@property
	def x(self):
		return self.points[0]
		
	@x.setter
	def x(self, value):
		self.points[0] = value

	@property
	def y(self):
		return self.points[1]
		
	@y.setter
	def y(self, value):
		self.points[1] = value
		
	def __getitem__(self, key):
		return self.points[key]
		
	def __setitem__(self, key, value):
		self.points[key] = value
		
	#def get_normalized_form(self):
	#	return Vector3d(self.x / 2, self.y / 2, self.z / 2)

class Vector3d(Vector2d):
	def __init__(self, x, y, z):
		self.points = [x, y, z]
		
	def cross_product(self, vector3d):
		# Returns a line that is perpendicular to the parameter
		# and self.
		# Returns the 'normal'.
		x = self.y * vector3d.z - self.z * vector3d.y
		y = self.z * vector3d.x - self.x * vector3d.z
		z = self.x * vector3d.y - self.y * vector3d.x
		
		return Vector3d(x, y, z)
		
	def dot_product(self, vector3d):
		# Returns a scalar that defines how similar two
		# vectors are to one another.
		return self.x * vector3d.x + self.y * vector3d.y + self.z * vector3d.z
		
	def vector_3d_length(self):
		return math.sqrt(self.dot_product(self))
		
	def subtract_3d(self, vector3d):
		return Vector3d(self.x - vector3d.x, self.y - vector3d.y, self.z - vector3d.z)
		
	def add_3d(self, vector3d):
		return Vector3d(self.x + vector3d.x, self.y + vector3d.y, self.z + vector3d.z)
		
	def divide_3d(self, value):
		return Vector3d(self.x / value, self.y / value, self.z / value)
		
	def get_normalized_form(self):
		length = self.vector_3d_length()
		return Vector3d(self.x / length, self.y / length, self.z / length)

	@property
	def z(self):
		return self.points[2]
		
	@z.setter
	def z(self, value):
		self.points[2] = value
			
class Vector4d(Vector3d):
	def __init__(self, x, y, z, w):
		self.points = [x, y, z, w]
		
	@property
	def w(self):
		return self.points[3]
		
	@w.setter
	def w(self, value):
		self.points[3] = value
		
	#def get_normalized_form(self):
	#	return Vector3d(self.x / 4, self.y / 4, self.z / 4)