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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Comparing Planes In Exercises 13-22, determine whether the planes

a 1 x   +   b 1 y   +   c 1 z   = d 1

and

a 2 x + b 2 y + c 2 z   =   d 2 are parallel, perpendicular, or neither. The planes are parallel when there exists a nonzero constant k such that a 1 =   k a 2 ,   b 1 =   k b 2 , and c 1 =   k c 2 , and are perpendicular when a 1 a 2 + b 1 b 2 + c 1 c 2 =   0.

x = 2 , y = 4

To determine

Whether the plane x=2 and y=4 are parallel, perpendicular or neither.

Explanation

Given Information:

The given planes are x=2 and y=4.

For the two planes a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2:

Condition for both the planes to be parallel:

a1=ka2,b1=kb2 and c1=kc2 (where ‘k’ is constant scalar)

Condition for both the planes to be perpendicular:

a1a2+b1b2+c1c2=0

Analyse the equation of planes and observe which condition they satisfy

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