Problem 7: The temperature T(x, y, z) is inversely proportional to the distance from the origin (0,0,0).
(a) Given that the temperature at the point (1, 2, 2) is 120 °C, obtain an expression for T(x, y, z).
(b) Show that, at any point in space, the direction of greatest increase in temperature is given by a vector that points toward the origin.