Fitting a 3D parametric line to 3D data

Hi,

Suppose I have data of 3D points in the form of 3 n by 1 vectors, X, Y and Z. I'd like to least-squares fit a 3D line to this data in the form of

|x = x0 + a .* t

y = y0 + b .* t

z = z0 + 0 .* t|

I.e, I'd like to constrain z to be constant and obtain x0, y0, z0, a and b. The formulation may be different, as long as z remains constrained.

Is there a quick way to do this without the curve fitting and statistics toolboxes?

Many thanks.