Suppose that the temperature distribution in a room is given by T = T(:I:,y, z). We do not know the function T(:1:,y, z) but we do know that at the point (1, 3,2) it is the case that T(1,3, 2) = 55, Tx(1,3, 2) : 1,Ty(1,3,2)= 2, and TZ(1,3, 2) = 3. (a) At (1, 3,2) in which direction is the temperature increasing most rapidly and at what rate? Write your direction as a unit vector. (b) Find the tangent plane to the level surface T(:1:, y, z) = 55 at the point (1, 3,2). Write your answer in the form am + by + cz = d. (c) A y moves through the room according to r(t) = (2 + cos(7rt),3 + sin(7rt),2t). How fast is the temperature the y experiences changing when it passes through the point (1,3, 2)? (By fast, we mean nd %