the plane given is

$\displaystyle x+2y+3z-10=0$

distance formula is $\displaystyle \sqrt{x^2+y^2+z^2}$

I know that the distance squared will have the same minimizers so I'll use that

I need to solve for z to get it into a two variable problem

$\displaystyle z= \frac{-1-2y+10}{3}$

now,

my squared distance is

$\displaystyle x^2+y^2+\left(\frac{-x-2y-10}{3}\right)^2$

now take gradient, solve for minimizers then sub-in and find distance

correct?