Lagrangian:

where the function we want to minimize is actually

, but it's easy to see that

and

have critical points at the same vector

.
Derivatives of the Lagrangian set equal to zero:




Substituting the first three equations into the fourth gives


Solving for

, we get a single critical point at

, which in turn gives the least distance between the plane and (0, 2, 5) of

.