#include <iostream>
#include <cstdlib>
#include <cmath>
#include "vec.h"
using namespace std;

int main()
{
	vec x(1, 0, 0);
	vec y(0, 1, 0);
	vec z(0, 0, 1);

	vec sum = x + y;
	cout << "The sum of x and y is ";
	sum.print();
	cout << ".\n";

	cout << "The midpoint of x and y is ";
	(sum / 2).print();      //division has lower precedence than dot
	cout << ".\n";

	double dot = x * y;
	cout << "The dot product of x and y is " << dot << ".\n";

	double theta = acos(dot / (x.length() * y.length()));	//in radians
	const double pi = 4 * atan2(1, 1);
	cout << "The angle between x and y is "
		<< theta / pi << "pi radians or "
		<< theta * 180 / pi << " degrees.\n";

	vec perpendicular = x ^ y;
	cout << "A vector perpendicular to x and y is ";
	perpendicular.print();
	cout << ".\n";

	if ((x ^= y) != z) {
		cerr << "Error: new value of x should be z.\n";
		return EXIT_FAILURE;
	}

	return EXIT_SUCCESS;
}