make this code work able instruction are given in picture #include using namespace std; double lerpSingle(double a, double b, double t) { if (t <= 0.5) return a+(b-a)*t; else return b-(b-a)*(1.0-t); }   // This is for linear interpolation Vector3 lerp(Vector3 u, Vector3 v, double t) { return Vector3(lerpSingle(u.x, v.x, t), lerpSingle(u.y, v.y, t), lerpSingle(u.z, v.z, t)); }   // This is for identifying if 4 vectors are coplanar   bool coplanar(Vector3 p, Vector3 q, Vector3 r, Vector3 s) { Vector3 ab = Vector3(q.x-p.x, q.y-p.y, q.z-p.z); Vector3 bc = Vector3(r.x-q.x, r.y-q.y, r.z-q.z); Vector3 cd = Vector3(s.x-r.x, s.y-r.y, s.z-r.z); if (dot(cross(ab,bc), cd) == 0) { return true; } else { return false; } }   Below are the helper function I have used for your reference   double dot(Vector3 u, Vector3 v) { double product = 0; product = u.x*v.x + u.y*v.y + u.z*v.z; } Vector3 cross(Vector3 u, Vector3 v) { double x = u.y * v.z - u.z * v.y; double y = u.z * v.x - u.x * v.z; double z = u.x * v.y - u.y * v.x; return Vector3(x,y,z); }   I have used below helper class   #include #include using namespace std; class Vector3 { public: double x; double y; double z; Vector3(double _x, double _y, double _z) { x = _x; y = _y; z = _z; } Vector3 normalized() { double mag = magnitude(); if (mag != 0.) { x /= mag; y /= mag; z /= mag; } return Vector3(x,y,z); } double magnitude() { return abs(sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2))); } };   //my main method   int main() { Vector3 p = Vector3(3, 2, -5); Vector3 q = Vector3(-1, 4, -3); Vector3 r = Vector3(-3, 8, -5); Vector3 s = Vector3(-3, 2, 1); bool test = coplanar(p,q,r,s); if (test) { cout << "yes"; } else { cout << "no"; } return 0; } Output: Question No 1: #include #include using namespace std;   class Vector3   {   //private:          public:         double x, y, z;         Vector3();         Vector3(double x, double y, double z);         double dot(Vector3 u, Vector3 v); //dot product         Vector3 cross(Vector3 u, Vector3 v); //cross product         Vector3 normalized(); //returns a vector pointing in the same direction with length 1         double magnitude(); //returns the length of the vector         Vector3 operator+(Vector3 &u);         Vector3 operator-(Vector3 &v);         Vector3 operator*(double value);         double getX();         double getY();         double getZ();   };   Vector3::Vector3()   {         this->x = 0;         this->y = 0;         this->z = 0;   }   Vector3::Vector3(double x, double y, double z)   {         this->x = x;         this->y = y;         this->z = z;   }   Vector3 Vector3::normalized()   {         double mag = magnitude();         if (mag != 0)         {               x = x / mag;               y = y / mag;               z = z / mag;         }         return Vector3(x, y, z);   }   double Vector3::magnitude()   {         double magni = abs(sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2)));         return magni;   }   double Vector3::dot(Vector3 u, Vector3 v)   {         double product = 0;         product = u.x*v.x + u.y*v.y + u.z*v.z;         return product;   }   Vector3 Vector3::cross(Vector3 u, Vector3 v)   {         double x = u.y * v.z - u.z * v.y;         double y = u.z * v.x - u.x * v.z;         double z = u.x * v.y - u.y * v.x;         return Vector3(x, y, z);   }   Vector3 Vector3::operator+(Vector3 &v)   {         double x = this->x + v.x;         double y = this->y + v.y;         double z = this->z + v.z;         return Vector3(x, y, z);   }   Vector3 Vector3::operator-(Vector3 &v)   {         double x = this->x - v.x;         double y = this->y - v.y;         double z = this->z - v.z;         return Vector3(x, y, z);   }   Vector3 Vector3::operator*(double value)   {         double x = this->x * value;         double y = this->y * value;         double z = this->z * value;         return Vector3(x, y, z);   }   double Vector3::getX()   {         return this->x;   }   double Vector3::getY()   {         return this->y;   }   double Vector3::getZ()   {         return this->z;   }   Vector3 getOriginalVector(Vector3 vertices[], int numVertices)   {         Vector3 vec(0, 0, 0);         Vector3 vect1, vect2, vect3;         for (int i = 0; i < numVertices-2; i++)         {               Vector3 v1 = vertices[i];               Vector3 v2 = vertices[(i + 1) % numVertices];               vect1 = (vertices[i + 1] - vertices[i]);               vect2 = (vertices[i + 2] - vertices[i + 1]);               vect3 = (vec.cross(vect1, vect2));               vec = vec + vect3;         }         vect1 = (vertices[numVertices - 1] - vertices[numVertices - 2]);         vect2 = (vertices[0] - vertices[numVertices - 1]);         vect3 = (vec.cross(vect1, vect2));         vec = vec + vect3;         return vec.normalized();   }   int main()   {         int const numVertices = 5;         Vector3 vertices[numVertices] = { Vector3(2.0, 0.0, 0.0), Vector3(2.0, 2.0, 0.0),                                             Vector3(1.0, 2.0, 0.0), Vector3(0.0, 2.0, 0.0),                                             Vector3(0.0, 0.0, 2.0) };         Vector3 n = getOriginalVector(vertices, numVertices);         cout << "originalVector = (" << n.getX() << ", " << n.getY() << ", " << n.getZ() << ")\n";                return 0;   }