Zaphod Beeblebrox was in trouble after the infinite improbability drive caused the Heart of Gold, the spaceship Zaphod had stolen when he was President of the Galaxy, to appear between a small insignificant planet and its hot sun. The temperature of the ship's hull is given by \(T(x, y, z)=\) \(e^{-k\left(x^{2}+y^{2}+z^{2}\right)}\) Nivleks. He is currently at \((1,1,1)\), in units of globs, and \(k=2\) globs \(^{-2}\). (Check the Hitchhikers Guide for the current conversion of globs to kilometers and Nivleks to Kelvin.)

a. In what direction should he proceed so as to decrease the temperature the quickest?

b. If the Heart of Gold travels at \(e^{6}\) globs per second, then how fast will the temperature decrease in the direction of fastest decline?