Question

implement a C++ class name Vector. The Vector class contains a private double array of length 2 named elements that represents a two-dimensional vector. We will also implement an overloaded multiplication operator (*) that accepts a single Vector variable by reference and returns the Dot Product between the current Vector object and the one pointed to by the function argument in form of a double.

Please recall that the dot product of two vectors a =(21,92) and 5 = (b1,b2) is equal to a real scalar, which is calculated as: c=21b1 + a2b2 You are also to overload the addition (+) and subtraction (operators in order to calculate the summation and subtraction of two vectors from each other. Please note that both of these overloaded operators must accept a single Vector variable by reference and return another Vector object by value according to the following equations: a + 5 = (a1 +61, 22+62) à-b=(Q1-b1, 22-62) Your submission must be named "main.cpp", and must be submitted prior to the due date to be considered.

Answer 1

Below is the code for above problem. I have added the main function to test the Vector class. I have also added comments to explain what each statement does.

I have included the screenshots of the code and the sample output.

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C++ code :

#include <iostream>

using namespace std;

// Vector class
class Vector {
  
   private :
      
       // a double array representing a 2D vector
       double elements[2];
      
   public :
      
       // empty constructor
       Vector() {
          
       }
      
       // parameterized constructor to initialize a Vector
       Vector(double elem1, double elem2) {
          
           this->elements[0] = elem1;
           this->elements[1] = elem2;
       }
      
       // overriding the multiplication(*) operator
       double operator*(const Vector& vect) {
          
           // variable to store the dot product
           double dotProduct;
          
           // calculate the dot product
           dotProduct = (this->elements[0] * vect.elements[0]) + (this->elements[1] * vect.elements[1]);
          
           // return the calculated dot product
           return dotProduct;
       }
};

// main function to test the Vector class
int main() {
  
   // initialize the first vector
   Vector first(1.5, 2.8);
  
   // initialize the second vector
   Vector second(2.4, 5.9);
  
   /* calculate the dot product of the two vectors
       using the overloaded multiplication(*) operator
   */
   double product = first * second;
  
   // print the calculated dot product
   cout << "The dot product is : " << product;
}

Screenshots of the code :

1)

[*] Vector.cpp 1 #include <iostream> 2 3 using namespace std; 4. 5 // Vector class 6 class Vector { 8 private : // a double array representing a 2D vector double elements[2]; public : // empty constructor Vector() { } Il parameterized constructor to initialize a Vector Vector (double elem1, double elem2) { 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 this->elements[0] = elem1; this->elements[1] = elem2; } // overriding the multiplication(*) operator double operator* (const Vector& vect) { // variable to store the dot product double dotProduct; // calculate the dot product dotProduct = (this->elements[0] * vect.elements[0]) + (this->elements[1] * vect.elements[1]); // return the calculated dot product return dotProduct; Activate Windows Go to Settings to activate Windows. } }; 8 Compiler Resources alth Compile Log Debug Find Results Line: 47 Col: 36 Sel: 0 Lines: 57 Length: 1202 Insert Press Ctrl+F11 to toggle fullscreen or Ctrl+F12 to toggle toolbars

2)

Screenshot of the sample outptut :