Kindly use proper mathematical notation and detailed steps and working to provide the answer. Explanation of certain steps would be appreciated. Thank you.

(Rubric applies) The temperature T in a metal ball is inversely proportional to the distance from the centre of the ball. Take the centre of the metal ball to be the origin. The temperature at the point (1,2, 2) is measured to be 120. [a.] Find T = T(a', y, z}. [b] Find the gradient of T at the point (1, 2,2). [0.] Find the rate of change of T at (1,2, 2) in the direction toward the point (2,1,3). [d.] Show that at any point P in the ball, the direction of the greatest increase in temper- ature is given by a vector that points toward the origin