public class Vector3D
    {
        public float X;
        public float Y;
        public float Z;

        public Vector3D(float x, float y, float z)
        {
            X = x;
            Y = y;
            Z = z;
        }

        public Vector3D()
        {
            X = 0;
            Y = 0;
            Z = 0;
        }

        public bool IsValid()
        {
            return ((X == 0) && (Y == 0) && (Z == 0)) ? false : true;
        }

        public Vector3D Normalize()
        {
            double length = Math.Sqrt(X * X + Y * Y + Z * Z);
            var v = new Vector3D();
            v.X = (float)(X / length);
            v.Y = (float)(Y / length);
            v.Z = (float)(Z / length);
            return v;
        }

        public override string ToString()
        {
            return string.Format("{0}|{1}|{2}", X, Y, Z);
        }

        public static bool operator ==(Vector3D v1, Vector3D v2)
        {
            return v1.X == v2.X && v1.Y == v2.Y && v1.Z == v2.Z;
        }

        public static bool operator !=(Vector3D v1, Vector3D v2)
        {
            return !(v1 == v2);
        }

        public static Vector3D operator *(Vector3D v, float n)
        {
            return new Vector3D(v.X * n, v.Y * n, v.Z * n);
        }

        public static float operator *(Vector3D v1, Vector3D v2)
        {
            float f;
            f = v1.X * v2.X + v1.Y * v2.Y + v1.Z * v2.Z;
            return f;
        }

        public static Vector3D operator +(Vector3D v1, Vector3D v2)
        {
            return new Vector3D(v1.X + v2.X, v1.Y + v2.Y, v1.Z + v2.Z);
        }

        public static Vector3D operator -(Vector3D v1, Vector3D v2)
        {
            var v3 = new Vector3D((v1.X - v2.X), (v1.Y - v2.Y), (v1.Z - v2.Z));
            return v3;
        }

        public bool Equals(Vector3D obj)
        {
            if (ReferenceEquals(null, obj))
            {
                return false;
            }
            if (ReferenceEquals(this, obj))
            {
                return true;
            }
            return obj.X == X && obj.Y == Y && obj.Z == Z;
        }

        public override bool Equals(object obj)
        {
            if (ReferenceEquals(null, obj))
            {
                return false;
            }
            if (ReferenceEquals(this, obj))
            {
                return true;
            }
            if (obj.GetType() != typeof(Vector3D))
            {
                return false;
            }
            return Equals((Vector3D)obj);
        }

        public override int GetHashCode()
        {
            unchecked
            {
                int result = X.GetHashCode();
                result = (result * 397) ^ Y.GetHashCode();
                result = (result * 397) ^ Z.GetHashCode();
                return result;
            }
        }
    }