If θ is the angle between 1 x + 1 = 2 y − 1 = 2 z − 2 and the plane 2 x − y + λ z + 4 = 0 and is such that sin θ = 3 1 , the value of λ is

sin θ = 3 5 + λ 2 − 2 + 2 λ = 3 1 , so 4 λ = 5 + λ and λ = 3 5 .

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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryPlaneMedium2 minQB

MathematicsMediumsingle choice

If $θ$ is the angle between $\frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2}$ and the plane $2 x - y + λ z + 4 = 0$ and is such that $sin θ = \frac{1}{3}$ , the value of $λ$ is

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Answer:

Solution:

$sin θ = \frac{2 - 2 + 2 λ}{3 5 + λ} = \frac{1}{3}$ , so $4 λ = 5 + λ$ and $λ = \frac{5}{3}$ .

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Plane

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