A) The co-ordinates of points are given by


i) Explain why the totality of points given by the equation form a surface.
ii)Find the unit normal to the surface at any point (u,v).

B) If the temperature at any point with co-ordinates (x,y,z) is given by the expression
T = xy + 2yz + 3xz

i) What is the direction and magnitude of greatest change in temperature per unit distance
(1,1,1)?

ii) Find the change in temperature per unit distance at the point (1,1,1), in the direction



C) Evaluate