If - x-4y-5z-7 and 4x-4- y-10z-14-0 represent the same plane- then the value of - is equal to

Name: JEE- Grade 12- Mathematics- Three Dimensional Geometry- Session 09- W16
Uploaded: 2022-07-04T10:36:42+05:30
Description: Given equations represent the same plane nbsp; ∴a_1a_2=b_1b_2=c_1c_2=d_1d_2 ⇒λ4=510⇒λ=2 ...

Given equations represent the same plane nbsp; ∴a_1a_2=b_1b_2=c_1c_2=d_1d_2 ⇒λ4=510⇒λ=2 ...

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Byju's Answer

Standard XII

Mathematics

Definition of Function

If λ x+4y+5z=...

Question

If $λ x + 4 y + 5 z = 7$ and $4 x + 4 λ y + 10 z - 14 = 0$ represent the same plane, then the value of $λ$ is equal to

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Solution

Given equations represent the same plane
$∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{d_{1}}{d_{2}} \Rightarrow \frac{λ}{4} = \frac{5}{10} \Rightarrow λ = 2$

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Definition of Function

Standard XII Mathematics

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If λx+4y+5z=7 and 4x+4λy+10z−14=0 represent the same plane, then the value of λ is equal to

Given equations represent the same plane ∴a1a2=b1b2=c1c2=d1d2⇒λ4=510⇒λ=2

If $λ x + 4 y + 5 z = 7$ and $4 x + 4 λ y + 10 z - 14 = 0$ represent the same plane, then the value of $λ$ is equal to

Given equations represent the same plane
$∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} = \frac{d_{1}}{d_{2}} \Rightarrow \frac{λ}{4} = \frac{5}{10} \Rightarrow λ = 2$