Need help figuring out what the read_vector and write_vector functions are askin

Question

Need help figuring out what the read_vector and write_vector functions are asking for. Here is the prompt:

A 2D vector (u, v) has its base at the origin in the cartesian coordinate system, i.e.

the x-y axes, and its tip (or arrow) at x = u and y = v. Thus, a 2D vector can be

represented simply as an (x; y) point in the cartesian coordinate system. Write a program

that reads in a pair of 2D vectors and a scalar value and then applies the following vector

operations: addition, subtraction, scalar multiplication, and perpendicularity. The main

routine of the program is already provided in vector2D_template.cpp (which you copied

into vector2D.cpp). Your task is to add eight functions read_vector(), vector_length(),

write_vector(), vector_add(), vector_subtract(), scalar_mult(), normalize(), and

perpendicular() so that the program produces the desired results.

This is the template

/*

File: vector2D.cpp

Created by: ??

Creation Date: ??

Synopsis: ??

*/

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;

const double EPSILON(1e-12);

// function prototypes

// ENTER FUNCTION PROTOTYPE FOR read_vector HERE.

// ENTER FUNCTION PROTOTYPE FOR vector_length HERE.

// ENTER FUNCTION PROTOTYPE FOR write_vector HERE.

// ENTER FUNCTION PROTOTYPE FOR vector_add HERE.

// ENTER FUNCTION PROTOTYPE FOR vector_subtract HERE.

// ENTER FUNCTION PROTOTYPE FOR scalar_mult HERE.

// ENTER FUNCTION PROTOTYPE FOR normalize HERE.

// ENTER FUNCTION PROTOTYPE FOR perpendicular HERE.

// *** DO NOT CHANGE ANY CODE IN THE MAIN FUNCTION.

int main()

{

double u1, v1; // coordinates of first vector

double u2, v2; // coordinates of second vector

double u3, v3;

double scalar;

read_vector("Enter first vector (2 floats): ", u1, v1);

read_vector("Enter second vector (2 floats): ", u2, v2);

cout << "Enter scalar multiplier: ";

cin >> scalar;

cout << endl;

write_vector("First vector: ", u1, v1);

write_vector("Second vector: ", u2, v2);

cout << endl;

vector_add(u1, v1, u2, v2, u3, v3);

write_vector("Vector add: ", u3, v3);

vector_subtract(u1, v1, u2, v2, u3, v3);

write_vector("Vector subtract: ", u3, v3);

scalar_mult(u1, v1, scalar, u3, v3);

write_vector("Scalar multiplier: ", u3, v3);

cout << endl;

write_vector("First vector: ", u1, v1);

write_vector("Second vector: ", u2, v2);

perpendicular(u1, v1, u2, v2);

return(0);

}

// DEFINE FUNCTION read_vector HERE.

// DEFINE FUNCTION vector_length HERE.

// DEFINE FUNCTION write_vector HERE.

// DEFINE FUNCTION vector_add HERE.

// DEFINE FUNCTION vector_subtract HERE.

// DEFINE FUNCTION scalar_mult HERE.

// DEFINE FUNCTION normalize HERE.

// DEFINE FUNCTION perpendicular HERE.

Explanation / Answer

#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;
const double EPSILON(1e-12);

// function with prototypes
void read_vector (const string & prompt, double & x, double & y);    // ENTER THE FUNCTION OF PROTOTYPE FOR read_vector HERE.
double vector_length (double x, double y);                                       // ENTER THE FUNCTION OF PROTOTYPE FOR vector_length HERE.
void write_vector (const string & prompt, double & x, double & y);   // ENTER THE FUNCTION OF PROTOTYPE FOR write_vector HERE.
void vector_add (double x1, double y1, double x2, double y2, double & x3, double & y3); // ENTER THE FUNCTION OF PROTOTYPE FOR vector_add HERE.
void vector_subtract (double x1, double y1, double x2, double y2, double & x3, double & y3); // ENTER THE FUNCTION OF PROTOTYPE FOR vector_subtract HERE.
void scalar_mult (double x1, double y1, double s, double & x2, double & y2); // ENTER THE FUNCTION OF PROTOTYPE FOR scalar_mult HERE.
void normalize (double & x, double & y);                                                  // ENTER THE FUNCTION OF PROTOTYPE FOR normalize HERE.
void perpendicular (double & x1, double & y1, double & x2, double & y2); // ENTER THE FUNCTION OF PROTOTYPE FOR perpendicular HERE.

// *** DO NOT CHANGE ANY CODE IN THE MAIN FUNCTION.

int main()
{
double u1, v1; // coordinates of first vector
double u2, v2; // coordinates of second vector double u3, v3;
double scalar;
read_vector("Enter first vector (2 floats): ", u1, v1);
read_vector("Enter second vector (2 floats): ", u2, v2);
cout > scalar; cout << endl;
write_vector("First vector: ", u1, v1);
write_vector("Second vector: ", u2, v2);
cout << endl; vector_add(u1, v1, u2, v2, u3, v3);
write_vector("Vector add: ", u3, v3);
vector_subtract(u1, v1, u2, v2, u3, v3);
write_vector("Vector subtract: ", u3, v3);
scalar_mult(u1, v1, scalar, u3, v3);
write_vector("Scalar multiplier: ", u3, v3);
cout << endl; write_vector("First vector: ", u1, v1);
write_vector("Second vector: ", u2, v2);
perpendicular(u1, v1, u2, v2);
return(0);
}

void read_vector (const string & prompt, double & x, double & y) // DEFINE THE FUNCTION read_vector HERE.
{
    cout << prompt;
    cin >> x >> y;
}

double vector_length (double x, double y) // DEFINE THE FUNCTION vector_length HERE.
{
    double v_length = sqrt(pow(x, 2) + pow(y, 2));
    return (v_length);
}

void write_vector (const string & prompt, double & x, double & y) // DEFINE THE FUNCTION write_vector HERE.
{
    cout << "(" << x << ", " << y << ") has length " << vector_length(x,y) << endl;
}

void vector_add (double x1, double y1, double x2, double y2, double & x3, double & y3) // DEFINE THE FUNCTION vector_add HERE.
{
    x3 = x1 + x2;
    y3 = y1 + y2;
    cout << "The Vector add: ";
}

void vector_subtract (double x1, double y1, double x2, double y2, double & x3, double & y3) // DEFINE THE FUNCTION vector_subtract HERE.
{
    x3 = x1 - x2;
    y3 = y1 - y2;
    cout << "TheVector subtract: ";
}

void scalar_mult (double x1, double y1, double s, double & x2, double & y2) // DEFINE THE FUNCTION scalar_mult HERE.
{
    x2 = s * x1;
    y2 = s * y1;
    cout << "The Vector multiplier: ";
}

void normalize (double & x, double & y) // DEFINE THE FUNCTION normalize HERE.
{
    double v = vector_length(x, y);
  
    if (v < EPSILON)
    {
        x = x / v;
        y = y / v;
    }
}

void perpendicular (double & x1, double & y1, double & x2, double & y2) // DEFINE THE FUNCTION perpendicular HERE.
{
    normalize(x1, y1);
    normalize (x2, y2);
  
    double p1x = -y1;
    double p1y = x1;
    double p2x = -p1x;
    double p2y = -p1y;
  
    if (abs(x2 - p1x) < EPSILON && abs(y2 - p1y) < EPSILON || (abs(x2 - p2x) < EPSILON && abs(y2 - p2y) < EPSILON))
    {
        cout << "The Vectors are PERPENDICULAR." << endl;
    }
    else
    {
        cout << "The Vectors are NOT PERPENDICULAR." << endl;
    }
}

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