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2 answers:
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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 
.
where the function we want to minimize is actually
Derivatives of the Lagrangian set equal to zero:
Substituting the first three equations into the fourth gives
Solving for
I used a triangle generator, see picture attached
