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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryFamily of planesMedium2 minQB

MathematicsMediumsingle choice

An equation of the plane passing through the line of intersection of the planes $x + y + z = 6$ and $2 x + 3 y + 4 z + 5 = 0$ and the point $(1, 1, 1)$ is

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Any plane through the line of intersection is $2 x + 3 y + 4 z + 5 + λ (x + y + z - 6) = 0$ . It passes through $(1, 1, 1)$ if $(2 + 3 + 4 + 5) + λ (1 + 1 + 1 - 6) = 0$ , so $λ = \frac{14}{3}$ . The required plane is $20 x + 23 y + 26 z = 69$ .

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Family of planes

⏱ 2mℹ️ Source: QB

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