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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

https://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.

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