Jacobian of 2D element in 3D domain

I know how to calculate Jacobian matrix for 2D elements in 2D and for 3D elements in 3D.
But for any 2d element(a quadrilateral element) which is embedded in 3D space, how do I calculate this Jacobian? If I use a traditional method for calculation, then my Jacobian matrix is a 2*3 matrix. Then how do I calculate its determinant ?

PS: I am solving a finite element method where my physical space is in (x,y,z) and isoparametric space is in (ξ,n). For calculating the element stiffness matrices, I would need the determinant of the Jacobian but I could not figure out for this particular case.

Thank you in advance !