class vector{

private double x_component;
private double y_component;

public

vector()
{
	x_component=0.0;
        y_component=0.0;
}

vector(double x,double y)
{
	x_component=x;
        y_component=y;
}

double dotproduct(vector v)
{
	double res;
        res=(this.x_component*v.x_component)+(this.y_component*v.y_component);
        return res;
}

double magnitude()
{
	double mag;
        mag=Math.pow(this.x_component,2)+Math.pow(this.y_component,2);
        mag=Math.sqrt(mag);
        return mag;
}
         
double angle(vector v)
{
       double dot_prod,mag,mag1;
       double angle;
       
       dot_prod=dotproduct(v);
       mag=v.magnitude();
       mag1=this.magnitude();
       angle=Math.acos(dot_prod/(mag*mag1));
       angle=Math.toDegrees(angle);
 
       return angle;
}

vector add(vector v)
{
	vector res;
        double x,y;
        x=this.x_component + v.x_component;
        y=this.y_component + v.y_component; 
        res = new vector(x,y);

        return res;
}   	
 
vector subtract(vector v)
{
      	vector res;
        double x,y;
        x=this.x_component - v.x_component;
        y=this.y_component - v.y_component;
        res = new vector(x,y);

        return res;
}

vector scalerMultiply(double alpha)
{
	vector res;
        double x,y;
        x=alpha*this.x_component;
        y=alpha*this.y_component;
        res = new vector(x,y);
        return res;
}

vector unitVector()
{
	vector res;
        double x,y,mag;
        mag=this.magnitude();
        x=this.x_component/mag;
        y=this.y_component/mag;
        res = new vector(x,y);
     
        return res;
}

boolean isOrthogonal(vector v)
{
	double dot_prod;
        dot_prod = dotproduct(v);
        if(dot_prod==0.0)
           return true;
        else
           return false;
}

boolean isParallel(vector v)
{
	double ang;
        ang=this.angle(v);
        if(ang==0.0)
           return true;
        else
           return false;
}

void display_vector()
{
	System.out.println("The x_component "+this.x_component);
        System.out.println("The y_component "+this.y_component);
}

};


public class vectortest{

public static void main(String args[])
{
	double res,x1,y1,x2,y2,mag,mag1;
        vector a,b;
        vector unit,result_add,result_sub,result; 
        boolean flag; 
        long p; 

        x1=Integer.parseInt(args[0]);
        y1=Integer.parseInt(args[1]);
        
        x2=Integer.parseInt(args[2]);
        y2=Integer.parseInt(args[3]);

        a=new vector(x1,y1);
        b=new vector(x2,y2);

        res= a.dotproduct(b);
        System.out.println("The dot of the given vectors is "+res);

        res=a.magnitude(); 
        System.out.println("The magnitude of first vector is "+res);
        res=b.magnitude();
        System.out.println("The magnitude of second vector is "+res);

        result_add=a.add(b);
        System.out.println("A+B");  
        result_add.display_vector(); 
        System.out.println("A-B");
        result_sub=a.subtract(b);
        result_sub.display_vector();  

        result = result_add.unitVector();
        System.out.println("Unit vector in direction of A+B"); 
        result.display_vector();          
         
        res=a.angle(b);
        System.out.println("The angle in Degree between the vectors is "+res); 
        
        unit = new vector(1.0,1.0);
        flag=result_add.isOrthogonal(unit);
        if(flag==true)
               System.out.println("A+B and i+j are orthogonal");
        else
               System.out.println("A+B and i+j are not orthogonal");


        /* here we will first find the unit vector along the direction of A+B and then check 
           whether it is parallel to i-j or not */

        unit = new vector(1.0,-1.0);     
        result_add = result_add.unitVector();
        res=result_add.dotproduct(unit);
        mag=result_add.magnitude();
        mag1=unit.magnitude();
        p=Math.round(res/(mag*mag1)); 

        if(p==1)
               System.out.println("A+B and i-j are parallel");
        else
               System.out.println("A+B and i-j are not parallel");    
          
}

};