# Python | Implementing 3D Vectors using dunder methods

Dunder methods (double underscore) in Python are methods which are commonly used for operator overloading. Some examples of dunder methods are __init__ , __repr__ , __add__ , __str__ etc. These methods are useful to modify the behavior of an object.
For example, when ‘+’ operator is used between two numbers, the result obtained is simply the addition of the two numbers whereas when ‘+’ is used between two strings, the result obtained is the concatenation of the two strings.

Commonly used Vector operations:
Consider two vectors vec1 and vec2 with co-ordinates: vec1 = (x1, y1, z1) and vec2 = (x2, y2, z2).

• Magnitude: Magnitude of vec1 = .
• Addition: For this operation, we need __add__ method to add two Vector objects. where co-ordinates of vec3 are .
• Subtraction: For this operation, we need __sub__ method to subtract two Vector objects. where co-ordinates of vec3 are .
• Dot Product: For this operation, we need the __xor__ method as we are using ‘^’ symbol to denote the dot product. ^ where co-ordinates of vec3 are .
• Cross Product: For this operation, we need the __mul__ method as we are using ‘*’ symbol to denote the cross product. * where co-ordinates of vec3 are .

Finally, we also need a __init__ method to initialize the Vector co-ordinates and the __repr__ method to define the represenation of the Vector object. So when we print our Vector object, the output should be something like this. print(Vector(1, -2, 3)) ==> Output: 1i -2j + 3k

Below is the implementation :

 # Python3 program to implement 3-D Vectors.  from math import sqrt     # Definition of Vector class  class Vector:         # Initialize 3D Coordinates of the Vector      def __init__(self, x, y, z):          self.x = x          self.y = y          self.z = z         # Method to calculate magnitude of a Vector      def magnitude(self):             return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)         # Method to add to Vector      def __add__(self, V):             return Vector(self.x + V.x, self.y + V.y, self.z + V.z)         # Method to subtract 2 Vectors      def __sub__(self, V):             return Vector(self.x - V.x, self.y - V.y, self.z - V.z)         # Method to calculate the dot product of two Vectors      def __xor__(self, V):             return self.x * V.x + self.y * V.y + self.z * V.z         # Method to calculate the cross product of 2 Vectors      def __mul__(self, V):             return Vector(self.y * V.z - self.z * V.y,                        self.z * V.x - self.x * V.z,                        self.x * V.y - self.y * V.x)         # Method to define the representation of the Vector      def __repr__(self):             out = str(self.x) + "i "            if self.y >= 0:              out += "+ "         out += str(self.y) + "j "         if self.z >= 0:              out += "+ "         out += str(self.z) + "k"            return out        if __name__ == "__main__":         vec1 = Vector(1, 2, 2)      vec2 = Vector(3, 1, 2)         # Magnitude of vector1      print("Magnitude of vector1:", vec1.magnitude())         # String representation of vector      print("String represenation of vector1: " + str(vec1))         # Addition of two vectors      print("Addition of vector1 and vector2: " + str(vec1 + vec2))         # Subtraction of two vectors      print("Subtraction of vector1 and vector2: " + str(vec1 - vec2))         # Dot product of two vectors      print("Dot Product of vector1 and vector2: " + str(vec1 ^ vec2))         # Cross product of two vectors      print("Cross Product of vector1 and vector2: " + str(vec1 * vec2))

Output:

Magnitude of vector1: 3.0
String represenation of vector1: 1i + 2j + 2k
Addition of vector1 and vector2: 4i + 3j + 4k
Subtraction of vector1 and vector2: -2i + 1j + 0k
Dot Product of vector1 and vector2: 9
Cross Product of vector1 and vector2: 2i + 4j -5k


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