Problem for 13.1
Find all the vectors (Overscript[v,  ->])  
      in 3 dimensions having the length of 9 and the (Overscript[i,  ->])  component of (Overscript[v,  ->])  
      is 7 and the other two components of (Overscript[j,  ->])  
      and (Overscript[k,  ->])  are the same.

Solution : 
(9^2) = 
      (7^2) + (x^2) + (x^2) (pt 4)
x = 4 or  - 4 (pt2)
the possible vectors are
7  (Overscript[i,  ->])  + 
      4  (Overscript[j,  ->])  + 4  
            (Overscript[k,  ->])  (pt 2)

or 7  (Overscript[i,  ->])  - 4  (Overscript[j,  ->])  - 
      4  (Overscript[k,  ->])  (pt 2)

Problem for 14.2

Find all the partial derivatives of f (x, y, z) = (x^2) 
          (z^3) - 2  xy - 
        4  (y^3) 
          z  at the point of (1, 2, 3).

Solution : 
To fix  y and z,  
    we find
(Subscript[f, x]) (x, y, z) = 2  (xz^3) - 2  y (pt 2)

(Subscript[f, x]) (1, 2, 3) = 
      2*1*(3^3) - 2*2 (pt1)
=50

To fix x and z,  we find
(Subscript[f, y]) (x, y, z) =  -2 x - 
        12  (zy^2) (pt 2)

(Subscript[f, y]) (1, 2, 3) = -2 - 12*3*(2^2) (pt 1)

=-146

To fix x and y,  we find
(Subscript[f, z]) (x, y, z) = 3  (x^2) (z^2) (pt 2)

(Subscript[f, z]) (1, 2, 3) = 3*1*(3^2) (pt 1)

=27

If all the final results are correct,  
    they get another 1 point.