TITLE: Solution to Problem7
# !b1 Problem7:
 Is the distance between two parallel planes,
   Ax + By + Cz = D1 and Ax + By + Cz = D2
   given by |D1-D2| ?
   If not, what is the correct formula.
   Find the distance between the planes,
   x+y+2z=2 and x+y+2z=4.

!b3 SOLUTION:
By drawing the picture of two parallel planes with position
vectors u1 and u2 you can see that the distance between the planes
is NOT given by |D1-D2| but by the length of the projection of
(u2-u1) onto the normal to the planes. As a function dist this is,
> dis := (n,D1,D2) -> abs(D2-D1)/len(n):
# where len is just the length function,
> len := vec -> sqrt( innerprod(vec,vec) ):
# for the numbers in the problem,
> ans := dis([1,1,2],2,4);
                                            1/2
                                ans := 1/3 6

> evalf(%);
                                  .8164965809


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