Implement a data type Vector3D for three-dimensional vectors that has the same API as Vector, except that the constructor takes three double values as arguments. Also, add a cross-product method: the...

Implement a data type Vector3D for three-dimensional vectors that has the same API as Vector, except that the constructor takes three double values as arguments. Also, add a cross-product method: the cross-product of two vectors is another vector, defined by the equation

where c is the unit normal vector perpendicular to both a and b, and  is the angle between a and b. In Cartesian coordinates, the following equation defines the cross-product:

The cross-product arises in the definition of torque, angular momentum, and vector operator curl. Also, |a  b| is the area of the parallelogram with sides a and b.