Q3)(30 points) Suppose the function T(x, y, z) = 3 + xy - y + z - x describe the temperature at a point (x, y, z) in space with T(3,2,1) = 3. (a) Compute the directional derivative of T at (3,2,1) in the direction of the point (0,1,2). (b) At the point (3,2,1), in what direction does the temperature decrease most rapidly? (c) Moving along the curve given by x = 3e, y = 2 cost, z = 1+t, find dt' the rate of change of temperature with respect to t at t = 0. (d) Suppose i + 5j + ak is a vector that is tangent to the temperature level surface T(x, y, z) = 3 at (3,2,1). What is a?