# Min & Max in 3-D

Algebra Level pending

Suppose $$x$$, $$y$$ and $$z$$ are real numbers that satisfy $$x^2 + y^2 + z^2 = 2 .$$ If $$a$$ and $$b$$ are the minimum and maximum values of $$x + 3 y + 2 z ,$$ respectively, what is the value of $$-ab ?$$

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