SATHEE: 3D Geometry 3 Question 36

3D Geometry 3 Question 36

####36. The equation of the plane containing the lines $2 x - 5 y + z = 3, x + y + 4 z = 5$ and parallel to the plane $x + 3 y + 6 z = 1$ is

(2015 Main)

(a) $2 x + 6 y + 12 z = 13$

(b) $x + 3 y + 6 z = - 7$

(d) $2 x + 6 y + 12 x = - 13$

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Answer:

Correct Answer: 36. (c)

Solution:

Let equation of plane containing the lines

$\begin{aligned} 2 x - 5 y + z = 3 and x + y + 4 z & = 5 be \\ (2 x - 5 y + z - 3) + λ (x + y + 4 z - 5) & = 0 \\ \Rightarrow (2 + λ) x + (λ - 5) y + (4 λ + 1) z - 3 - 5 λ & = 0 \end{aligned}$

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 equations, we get

$6 + 3 λ = λ - 5 \Rightarrow 2 λ = - 11 \Rightarrow λ = - \frac{11}{2}$

On taking last two equations, we get

$6 λ - 30 = 3 + 12 λ \Rightarrow - 6 λ = 33 \Rightarrow λ = - \frac{11}{2}$

So, the equation of required plane is

$\begin{aligned} 2 - \frac{11}{2} x + \frac{- 11}{2} - 5 y + - \frac{44}{2} + 1 z - 3 + 5 \times \frac{11}{2} = 0 \\ \Rightarrow - \frac{7}{2} x - \frac{21}{2} y - \frac{42}{2} z + \frac{49}{2} = 0 \\ \Rightarrow x + 3 y + 6 z - 7 = 0 \end{aligned}$

3D Geometry 3 Question 36

Answer:

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3D Geometry 3 Question 36

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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