parallel planes
Which of the following planes are parallel? Are any of them identical?
P1: 4x - 2y - 6z = 3
P2: 4x - 2y - 2z = 6
P3: -6x + 3y -9z = 5
P4: z = 2x - y - 3
please explain each step in detail
© BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/identical-parallel-planes-8733
SOLUTION This solution is FREE courtesy of BrainMass!
a) Planes P1 & P2 Intersect. If you subtract P1 from P2 you will get 4z = 9. This means they have a point of intersection at Z = 2.25 and hence not parallel.
b) Planes P2 & P3 Intersect. if you multiply P2 by 1.4 AND p2+p3 , you will get -12z = 11.This means they have a point of intersection at Z = -11/12 and hence not parallel.
c)P2 and P4 are identical planes. If you rearrange P4 and multiply it by 2 you will get P2.
D) P1 and P3 intersect. If you multiply P1 by 1.5 AND ADD 1.5P1+P3 , you will get 0 = .5 , which means they do not intersect at all and a re parallel.
© BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddf>https://brainmass.com/math/calculus-and-analysis/identical-parallel-planes-8733