EXERCISES

1. A little Maple/Vector review: Let a := [ 2.015107659, 6.82972834313, -3.137831325 ], b := [ 3.28739322, -5.7418601463419, -1.4521786567 ], and c := [ 1.242627497, 6.85702448017, 1.86395490561]. Please use Maple to compute (when possible) the numerical value of the following expressions:
   1.  a + b
   2. (a b) (a + b)
   3. (a + b) (c (a + b))
   For those that can not be computed because they make no sense, please explain what is wrong. In addition, imagine for a moment evaluating those that make sense by hand or even using a traditional hand-held calculator. On the other hand, can you do better than Maple on any of these calculations? Is there an exact solution which Maple doesn't find? If so, how do you know? Why did Maple give a less-than perfect answer?

2. If a, b and c are three arbitrary three-dimensional, please show that
   a (b c ) = (a c) b - (a b) c