Here's the problem:
"Let lambda = a+b+c with (a,b,c)= (2,8,5)
Captain Astro is in trouble near the sunny side of Mercury. The temperature in degrees of her ship’s hull when she is at location (x, y, z) will be given by
T(x,y,z) = e^(-ax^2-by^2-cz^2)
where x, y, and z are measured in “space units”. Unfortunately, the metal of the hull will crack if the absolute value of the instantaneous rate of change of the temperature in a given direction is greater than sqrt(6)*e^(-lambda) degrees per space unit. Describe the set of possible directions in which she may proceed to leave the point (1,1,1) to decrease the temperature without cracking the hull of the ship. It would be helpful to Captain Astro to give a description of the set of possible directions in terms of a range of angles in degrees relative to some fixed vector (for example, 'go in any direction that makes an angle with the vector v = 2.2i-3.1j-5.72k that is between 27º and 67º.')"
I have no idea how to do solve this. Help?