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
>