The function is a solution to the heat equation and gives the temperature at the point in 3-space and time . the constant is the thermal conductivity of the medium through which the heat is flowing. (a) show that the function is a solution to the heat equation for all in 3-space and . (b) for each fixed time , what are the level surfaces of the function in 3-space? (c) regard as fixed and compute grad . what does grad tell us about the direction and magnitude of the heat flow?