#include <math.h>

struct vector{
        double x;
        double y;
        double z;
};
typedef struct vector vector;

double dotprod(vector a, vector b){
        return a.x*b.x + a.y*b.y + a.z*b.z;
}

vector crossprod(vector a, vector b){
        vector x;
        x.x = (a.y*b.z)-(b.y*a.z);
        x.y = (a.z*b.x)-(b.z*a.x);
        x.z = (a.x*b.y)-(b.x*a.y);
        return x;
}

double vectorlen(vector a){
        return sqrt((a.x*a.x) + (a.y*a.y) + (a.z*a.z));
}

vector vectorxd(vector a, double d)
{
   a.x *= d;
   a.y *= d;
   a.z *= d;
   return a;
}

vector vectorneg(vector a)
{
   return vectorxd(a, -1);
}


vector vectoradd(vector a, vector b)
{
   vector c;
   c.x = a.x + b.x;
   c.y = a.y + b.y;
   c.z = a.z + b.z;
   return c;
}

double vectorangle(vector a, vector b)
{
  return acos((dotprod(a, b)/(vectorlen(a)*vectorlen(b))));
}

vector unitvector(vector a){
        double len;
        if((len = vectorlen(a)) != 0){
                a.x /= len;
                a.y /= len;
                a.z /= len;
        }
        return a;
}

vector vectorproj(vector a, vector b){
        //Vektori a projisoidaan vektorille b
        return vectorxd(b, dotprod(a, b)/dotprod(b, b));
}

double scalarproj(vector a, vector b){
        return dotprod(a, b)/vectorlen(b);
}