// Example of using the vector library

#include <iostream.h> 
#include <math.h>
#include "vec3.h"

int main() { 

 Vec3 v0,v1,v2;
 cout << "enter three vectors";
 cin >> v0; cin >> v1; cin >> v2;

 cout << "Area of the parallelogram spanned by the first two vectors is: " 
      << cross(v0,v1).length() << endl;
 cerr << "Volume of the parallelogram spanned by the vectors is: " 
      << fabs(dot(cross(v0,v1),v2)) << endl;
 cerr << "Vectors along the edges of the triangle (v0,v1,v2): " 
      << "[" << v1-v0 << "] [" << v2-v1 << "] [" << v0-v2 << endl;
 cerr << "Normal to the plane of the triangle, unnormalized: [" 
      <<  cross(v1-v0, v2-v0) << "]" 
      << " normalized: [" << cross(v1-v0, v2-v0).dir() << "]" << endl;
 cerr << "Distance from v0 to the line connecting v1,v2 is:" << 
   ( v1-v0 - ( dot(v1-v0,v2-v1)/(v2-v1).dot() )*(v2-v1) ).length() << endl;
 return 0;
}