a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1 – Dz| d = |Ai + Bj + Ck| b) Find the distance between the planes 2x + 3y – z = 6 and 2x + 3y – z = 12.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 19EQ
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a) Show that the distance between the parallel planes Ax + By + Cz = D1 and
Ax + By + Cz = D2 is
|D1 - D2|
d =
|Ai + Bj + Ck|
b) Find the distance between the planes 2x + 3y – z = 6 and 2x + 3y – z = 12.
c) Find an equation for the plane parallel to the plane 2x – y + 2z = -4 if the
point (3,2, –1) is equidistant from the two planes.
d) Write equations for the planes that lie parallel to and 5 units away from the
plane x – 2y + z = 3.
Transcribed Image Text:a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1 - D2| d = |Ai + Bj + Ck| b) Find the distance between the planes 2x + 3y – z = 6 and 2x + 3y – z = 12. c) Find an equation for the plane parallel to the plane 2x – y + 2z = -4 if the point (3,2, –1) is equidistant from the two planes. d) Write equations for the planes that lie parallel to and 5 units away from the plane x – 2y + z = 3.
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