Create and type two 6 min 10pt questions for Ma3160 class.

12.4

Find the equation for the linear function through the three points 
	(-7, 3, -3), (0, 2, 1), and  (-3, 5, -11)

Pts  = {{-7, 3, -3}, {0,  
            2,  -1}, {-3,  
            5,  -11}};


    Plane[x_, y_] =  Fit[Pts, {1,  x ,  y}, {x, y}]

u  =  Pts[[1]] - Pts[[2]]
v  =  Pts[[1]] - Pts[[3]]
normal  =  Cross[u, v]

The equation of the plane is 
	4 (x + 7) + 64 (y - 3) + 18 (z + 3) = 
        0

Points:  I would award 3 points for calculating each of the vectors, u and v.  Three points to be awarded for correctly normallizing the two.  Finally, 1 point for the plane.

14.1

2.  Draw a  contour diagram for the linear function  f(x, y) if 

	a .   (Subscript[f, x])  > 0 and (Subscript[f, y]) > 0
	
	b .   (Subscript[f, x])<0 and (Subscript[f,  y])>0

Solution :  (Should be graphed with lines superimposed over the axes,  showing trends as follows)



    a .   function values will increase as you move up and to the right

      b .   function values will increase as you move  up and to the left








    Points :   Award 5 points for each graph .   A full 5 points should be awarded if the graph is clear and clearly shows increasing values drawn into the graph,  
    etc .   I would award 4 points if the intent was  clear,  
    but there wasn' t any indication of increasing values,  
    and so on . 

(Allan,  I tried to figure out how to make Mathematica give me the graphs to be used for the solutions .     Please take mercy on me.  :(           )