# 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 =  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 representation 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

 # 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 representation 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 representation 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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