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 = $\sqrt{(x1)^2 + (y1)^2 + (z1)^2}$ .
Addition: For this operation, we need __add__ method to add two Vector objects.
$vec1 + vec2 = vec3$ where co-ordinates of vec3 are $(x1+x2, y1+y2, z1+z2)$ .
Subtraction: For this operation, we need __sub__ method to subtract two Vector objects.
$vec1 - vec2 = vec3$ where co-ordinates of vec3 are $(x1-x2, y1-y2, z1-z2)$ .
Dot Product: For this operation, we need the __xor__ method as we are using ‘^’ symbol to denote the dot product. $vec1$ ^ $vec2 = vec3$ where co-ordinates of vec3 are $(x1*x2, y1*y2, z1*z2)$ .
Cross Product: For this operation, we need the __mul__ method as we are using ‘*’ symbol to denote the cross product. $vec1$ * $vec2 = vec3$ where co-ordinates of vec3 are $(y1*z2 - y2*z1, x1*z2 - x2*z1, x1*y2 - x2*y1)$ .

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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