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Solution to Problem7


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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

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Mon Feb 7 16:33:39 EST 2000