One or Multidimensional Root Finding?

[Olumide <50295@......>]

Hello,

I'm trying to find the point p(x,y,z) on an (nonlinear) implicit surface 
F(x,y,z) = 0 closest that is nearest to a given initial point q(x,y,z), 
the problem is that my reading of the docs makes the choice the class of 
root finding algorithm a bit difficult. According to the manual, 
multidimensional root-finding algorithms are for "solving nonlinear 
systems with n equations in n unknowns", while one dimensional 
Root-Finding algorithms are for "finding roots of arbitrary 
one-dimensional functions". The problem is that I have one equation 
F(x,y,z) = 0, with whose solution is a tuple or vector or group of 3 
numbers p(x,y,z). Which algorithm should I use to solve such a problem? 
A one dimensional or a multi-dimensional root solver?

Thanks,

- Olumide