A rectangle in 3-space, parallel to the xy-plane, has non-adjacent corners at points (2,2,3) and (-5,-4,3):

(a)  What must the other two corner points be?

(b)  I would like to construct a rectangular solid, containing the origin, with volume  = 
          210 (units^3) .   
 
              Using the rectangle from above as the top surface, \(what\ are\ the\ 4\ base\ points\ of\ the\ \(\(solid\)\(?\)\)\)

(c)  What is the surface area of the rectangular solid?

Answers:
(a)  (2, -4, 3) and (-5, 2, 3)     (b)  (-5, 2, -2),(2, -4, -2),(2, 2, -2) and (-5, -4, -2)      (c)  2(42)+ 2 (35)+2 (30) = 214 (units^2)

Some common problems that might arise with this problem are:
		the fact that there is no graph
		very wordy
		in this case, containing the origin means heading negative units along the z-axis, since the rectangle from (a) is above the xy-plane. 
		explaining the two points as "non-adjacent corners" could cause a few problems
		some may have problems finding the 4 base corners because the rectangular solid drops below the xy-plane into negative z-cooridinates

For the surface x=(y^3)(z^7) in 3-space;

	(a) Find the tangent to the surface at the point (1, -1, -1) .   Show all work for full credit.
   (b)Find a normal vector to the \(surface . 
	
\(Answers : 
\ \ \ \ \((a)\)\ \ x\  + \ 
                  3  y\  + \ 7  z\)\) = -9   (b) (Overscript[i,  ->])  +  (Overscript[(3  j),  ->]) + (Overscript[(7  k),  ->])

Some common problems that might arise with this problem are:
		not remembering the steps or formula for a tangent plane
		not remembering how to take partial derivatives (i.e. forgetting that the (z^7) in (y^3)(z^7)is a constant when taking the derivative with respect to y
		positive and negative numbers can always cause sign problems
		forgetting to do the second part, since the part (a) take more time