Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Find the equation of the plane mid-parallel to the planes 2x-3

Question

Find the equation of the plane mid-parallel to the planes $2 x - 3 y + 6 z + 21 = 0$ and $2 x - 3 y + 6 z - 14 = 0$ .

Views: 736 students

Found 6 tutors discussing this question

Sofia Discussed

Find the equation of the plane mid-parallel to the planes

2 x - 3 y + 6 z + 21 = 0

and

2 x - 3 y + 6 z - 14 = 0

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

As we know that

Distance between two parallel planes

a x + b y + cz + d_{1} = 0

and

a x + b y + cz + d_{2} = 0

\frac{∣ d _{2} - d _{1} ∣}{a ^{2} + b ^{2} + c ^{2}}

Given equation of planes are

2 x - 3 y + 6 z + 21 = 0 \dots (1)

2 x - 3 y + 6 z - 14 = 0 \dots (2)

The equation of the plane mid -parallel to above planes will be of the form

2 x - 3 y + 6 z + k = 0 \dots (3)

⟹

Distance between

(1) & (3) =

Distance between

(2) & (3)

⟹ \frac{∣ k - 21∣}{2 ^{2} + ( - 3 ) ^{2} + 6 ^{2}} = \frac{∣ k + 14∣}{2 ^{2} + ( - 3 ) ^{2} + 6 ^{2}}

⟹ ∣ k - 21∣ = ∣ k + 14∣

⟹ k - 21 = k + 14

k - 21 = - (k + 14)

⟹ - 21 = 14 (false)

k - 21 = - k - 14

⟹ 2 k = 7

⟹ k = \frac{7}{2}

(3)

will become

2 x - 3 y + 6 z + \frac{7}{2} = 0 ⟹ 4 x - 6 y + 12 z + 7 = 0

The equation of mid-parallel plane is

4 x - 6 y + 12 z + 7 = 0

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Find the equation of the plane mid-parallel to the planes $2 x - 3 y + 6 z + 21 = 0$ and $2 x - 3 y + 6 z - 14 = 0$ .
Answer Type	Text solution:1
Upvotes	150