/// <summary>
    /// 向量類
    /// </summary>
    public class Vector
    {
        public double x, y, z;

        public Vector()
        {

        }

        public Vector(double _x, double _y, double _z)
        {
            x = _x;
            y = _y;
            z = _z;
        }

        /// <summary>
        /// 求向量長度
        /// </summary>
        /// <returns></returns>
        public double magnitude()
        {
            return Math.Sqrt(x * x+ y * y+z * z);
        }

        /// <summary>
        /// 求單位向量
        /// </summary>
        /// <returns></returns>
        public Vector normal()
        {
            double k = 1 / magnitude();
            Vector d = new Vector(k * x, k * y, k * z);
            return d;         
        }
        
        /// <summary>
        /// 向量和
        /// </summary>
        /// <param name="v1">向量1</param>
        /// <param name="v2">向量2</param>
        /// <returns>新向量</returns>
        public static Vector operator +(Vector v1, Vector v2)
        {
            Vector d = new Vector(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z);
            return d;
           
        }
        /// <summary>
        /// 求反向量
        /// </summary>
        /// <param name="v">向量</param>
        /// <returns>新向量</returns>
        public static Vector operator -(Vector v)
        {
            Vector d = new Vector(-v.x, -v.y, -v.z);
            return d;
           
        }
        /// <summary>
        /// 求向量
        /// </summary>
        /// <param name="v1"></param>
        /// <param name="v2"></param>
        /// <returns></returns>
        public static Vector operator -(Vector v1, Vector v2)
        {
            Vector d = new Vector(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z);
            return d;            
        }

        public static Vector operator *(Vector v, double k)
        {
            Vector d = new Vector(k * v.x, k * v.y, k * v.z);
            return d;
            
        }
        public static Vector operator *(double k, Vector v)
        {
            Vector d = new Vector(k * v.x, k * v.y, k * v.z);
            return d;
            
        }
        public static Vector operator /(Vector v, double k)
        {
            Vector d=new Vector(v.x / k, v.y / k, v.z / k) ;
            d.x =v.x / k;
            d.y =v.y / k;
            d.z =v.z / k;
            return d;          
        }

        public static double operator ^(Vector v1, Vector v2)
        {
            return v2.x + v2.x + v1.y + v2.y + v1.z + v2.z;
        }
        public static Vector operator *(Vector v1, Vector v2)
        {
            Vector d = new Vector(v1.y * v2.z - v2.z * v2.y,
                v1.z * v2.x - v1.x * v2.z,
                v1.x * v2.y - v1.y * v2.x);
            return d;           
        }              
    }