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The equation of the plane containing the line 2 x-5 y+z=3, x+y

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Solving time: 4 mins

The equation of the plane containing the line $2 x - 5 y + z = 3, x + y + 4 z = 5$ and parallel to the plane $x + 3 y + 6 z = 1$ is (a) $2 x + 6 y + 12 z = 13$ (b) $x + 3 y + 6 z = - 7$ (c) $x + 3 y + 6 z = 7$ (d) $2 x + 6 y + 12 z = - 13$

Name: Video solution 1: The equation of the plane containing the line 2x−5y+z=3,x+y+4z=5 and parallel to the plane x+3y+6z=1 is (a) 2x+6y+12z=13 (b) x+3y+6z=−7 (c) x+3y+6z=7 (d) 2x+6y+12z=−13
Uploaded: 2022-11-30T03:44:19.000Z
Duration: 15 min
Description: Video solution 1: The equation of the plane containing the line 2x−5y+z=3,x+y+4z=5 and parallel to the plane x+3y+6z=1 is (a) 2x+6y+12z=13 (b) x+3y+6z=−7 (c) x+3y+6z=7 (d) 2x+6y+12z=−13

Views: 5,235 students

Updated on: Nov 30, 2022

Book:

Arihant JEE Main Chapterwise Solutions Mathematics (2019-2002) (Arihant)

Exam:

JEE Mains 2015

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Olivia Discussed

The equation of the plane containing the line

2 x - 5 y + z = 3, x + y + 4 z = 5

and parallel to the plane

x + 3 y + 6 z = 1

is (a)

2 x + 6 y + 12 z = 13

(b)

x + 3 y + 6 z = - 7

(c)

x + 3 y + 6 z = 7

(d)

2 x + 6 y + 12 z = - 13

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Exp. (c) Let equation of plane containing the lines

2 x - 5 y + z = 3 and x + y + 4 z = 5 be

(2 x - 5 y + z - 3) + λ (x + y + 4 z - 5) = 0

\Rightarrow (2 + λ) x + (λ - 5) y + (4 λ + 1) z - 3 - 5 λ = 0

......(i) This plane is parallel to the plane

x + 3 y + 6 z = 1

∴ \frac{2 + λ}{1} = \frac{λ - 5}{3} = \frac{4 λ + 1}{6}

On taking first two equalities, we get

6 + 3 λ = λ - 5

\Rightarrow 2 λ = - 11

\Rightarrow λ = - \frac{11}{2}

On taking last two equalities, we get

6 λ - 30 = 3 + 12 λ

\Rightarrow - 6 λ = 33 \Rightarrow λ = - \frac{11}{2}

So, the equation of required plane is

(2 - \frac{11}{2}) x + (\frac{- 11}{2} - 5) y + (- \frac{44}{2} + 1) z - 3 + 5 \times \frac{11}{2} = 0

\Rightarrow - \frac{7}{2} x - \frac{21}{2} y - \frac{42}{2} z + \frac{49}{2} = 0

\Rightarrow x + 3 y + 6 z - 7 = 0

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Question Text	The equation of the plane containing the line $2 x - 5 y + z = 3, x + y + 4 z = 5$ and parallel to the plane $x + 3 y + 6 z = 1$ is (a) $2 x + 6 y + 12 z = 13$ (b) $x + 3 y + 6 z = - 7$ (c) $x + 3 y + 6 z = 7$ (d) $2 x + 6 y + 12 z = - 13$
Updated On	Nov 30, 2022
Topic	Three Dimensional Geometry
Subject	Mathematics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	177
Avg. Video Duration	15 min

The equation of the plane containing the line $2 x - 5 y + z = 3, x + y + 4 z = 5$ and parallel to the plane $x + 3 y + 6 z = 1$ is (a) $2 x + 6 y + 12 z = 13$ (b) $x + 3 y + 6 z = - 7$ (c) $x + 3 y + 6 z = 7$ (d) $2 x + 6 y + 12 z = - 13$

Text solutionVerified

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The equation of the plane containing the line 2x−5y+z=3,x+y+4z=5 and parallel to the plane x+3y+6z=1 is (a) 2x+6y+12z=13 (b) x+3y+6z=−7 (c) x+3y+6z=7 (d) 2x+6y+12z=−13

Text solutionVerified

Filo tutor solutions (1)

Questions from JEE Mains 2015 - PYQs

Practice questions from Arihant JEE Main Chapterwise Solutions Mathematics (2019-2002) (Arihant)

Practice questions from Three Dimensional Geometry in the same exam

Practice more questions from Three Dimensional Geometry

Practice questions on similar concepts asked by Filo students

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The equation of the plane containing the line $2 x - 5 y + z = 3, x + y + 4 z = 5$ and parallel to the plane $x + 3 y + 6 z = 1$ is (a) $2 x + 6 y + 12 z = 13$ (b) $x + 3 y + 6 z = - 7$ (c) $x + 3 y + 6 z = 7$ (d) $2 x + 6 y + 12 z = - 13$