## 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. |

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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Carlos Rodriguez <carlos@math.albany.edu> Last modified: Mon Feb 7 16:33:39 EST 2000