v3.cpp

#include <iostream>
#include <cmath>
using namespace std;

class Vec3{

    public:

    float x;
    float y;
    float z;

    Vec3(float a=0, float b=0, float c=0){
        x = a;
        y = b;
        z = c;
    }

    float mag() const {
        return sqrt(x*x + y*y + z*z);
    }

    Vec3 operator+( const Vec3& B) const {
        return Vec3(x+B.x, y+B.y, z+B.z);
    }

    Vec3 operator-( const Vec3& B) const {
        return Vec3(x-B.x, y-B.y, z-B.z);
    }

    Vec3 operator*( const Vec3& B ) const {
        return Vec3( y*B.z - z*B.y , z*B.x - x*B.z , x*B.y - y*B.x );
    }

    Vec3 operator*( float k ) const {
        return Vec3( x*k, y*k, z*k );
    }

    Vec3 operator/( float k ) const {
        return Vec3( x/k, y/k, z/k );
    }

    float dot( const Vec3& B ) const {
        return x*B.x + y*B.y + z*B.z;
    }

    Vec3 cross( const Vec3& B ) const {
        return (*this) * B;
    }

    friend ostream& operator<<(ostream& os, const Vec3& v){
        os << "[x: " << v.x << ", y: " << v.y << ", z: " << v.z << "]";
        return os;
    }

    friend Vec3 operator*(float k, const Vec3& v){
        return v * k;
    }

    float angle( const Vec3& B ) const{
        return acos(dot(B) / (mag() * B.mag()));
    }

    Vec3 unit() const{
        float m = mag();
        if (m==0) return Vec3(0,0,0);
        return Vec3(x/m,y/m,z/m);
    }

    Vec3 project( const Vec3& B ) const{
        float mag2 = B.mag();
        if (mag2 == 0) return Vec3(0,0,0);
        return B * dot(B)/(mag2*mag2);
    }

};

int main() {

    Vec3 A(1,1,0);
    Vec3 B(1,0,0);

    cout << A.unit();

    return 0;

}