// contains all the vector operations that is given in the initialize() list
  static void operations(int choice) {
    Vector v1, v2;

    // switch statement determines what operation the user chose
    switch (choice) {
        // adds inputted vectors
      case 1:
        System.out.println("Enter the first vector:");
        v1 = new Vector();
        System.out.println("Enter the second vector:");
        v2 = new Vector();
        v1.addVectors(v2);
        break;
        // subtracts second inputted vector from the first
      case 2:
        System.out.println("Enter the first vector:");
        v1 = new Vector();
        System.out.println("Enter the second vector:");
        v2 = new Vector();
        v1.subtractVectors(v2);
        break;
        // finds the magnitude of the inputted vector
      case 3:
        System.out.println("Enter the vector:");
        v1 = new Vector();
        System.out.printf("magnitude: %.3f\n", v1.magnitude());
        break;
        // finds the product of an inputted vector with inputted scalar
      case 4:
        System.out.println("Enter the vector:");
        v1 = new Vector();
        v1.scalarProduct();
        break;
        // finds the dot product of two inputted vectors
      case 5:
        System.out.println("Enter the first vector:");
        v1 = new Vector();
        System.out.println("Enter the second vector:");
        v2 = new Vector();
        System.out.printf("Dot Product: %.3f\n", v1.dotProduct(v2));
        break;
        // finds the angle between the two inputted vectors
      case 6:
        System.out.println("Enter the first vector:");
        v1 = new Vector();
        System.out.println("Enter the second vector:");
        v2 = new Vector();
        v1.angle(v2);
        break;
    }
  }