#include <iostream>
#include <math.h>
#include <iomanip>

using namespace std;

float u[3], v[3], num, denom, dot_prod3;
double cos_theta, angle_radians, theta;
float pi = 3.141592653589;

//define two vectors, and the dot product
int i, j, n = 4;
int main(){

    for(j = 1; j < n; j++){
        // get x vector components
        cout<< "u_"<< j <<"= ? " <<flush;
        cin >> u[j];
        // get y vector components
        cout<< "v_"<< j <<"= ? " <<flush;
        cin >> v[j];
    }
    
    num = (u[1] * v[1]) + (u[2] * v[2]) + (u[3] * v[3]);
    
    denom = (sqrt((u[1] * u[1]) + (u[2] * u[2]) + (u[3] * u[3])))*
    (sqrt((v[1] * v[1]) + (v[2] * v[2]) + (v[3] * v[3])));
    
    cos_theta = num/denom;
    angle_radians = acos(cos_theta);
    theta = (angle_radians * 180)/pi;
    
    cout<<setprecision(2);
    cout <<"Angle is: "<< theta <<" degrees approx"<<endl;
        
    if(fabs(cos_theta) <= pow(10 , -6))
    cout<<"vectors are orthogonal"<<endl;
    
    cout<<"\n";
    
    return 0;
}