If the planes r ˉ ⋅ ( 2 i ^ − λ j ^ + k ^ ) = 3 and r ˉ ⋅ ( 4 i ^ − j ^ + μ k ^ ) = 5 are paralle, then values of λ and μ are respectively

The two planes are parallel hence 4 2 = − 1 − λ = μ 1 ⇒ λ = 2 1 and μ = 2

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryPlane (Equations)Easy2 minPYQ_2022

MathematicsEasysingle choice

If the planes $\overset{r}{ˉ} \cdot (2 \hat{i} - λ \hat{j} + \hat{k}) = 3$ and $\overset{r}{ˉ} \cdot (4 \hat{i} - \hat{j} + μ \hat{k}) = 5$ are paralle, then values of $λ$ and $μ$ are respectively

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Solution:

The two planes are parallel hence $\frac{2}{4} = \frac{- λ}{- 1} = \frac{1}{μ} \Rightarrow λ = \frac{1}{2} and μ = 2$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Plane (Equations)

⏱ 2mℹ️ Source: PYQ_2022

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