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. |
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