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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryFamily of planesMedium2 minQB

MathematicsMediummultiple choice

The plane $3 x + 4 y = 0$ is rotated through an angle of $π /4$ about its line of intersection with the $x y$ -plane. The equation of the plane in the new position is

Options:(select one or more)

Answer:

C, D

Solution:

The required plane is $3 x + 4 y + λ z = 0$ . The angle between it and $3 x + 4 y = 0$ is $\frac{π}{4}$ : $cos \frac{π}{4} = \frac{25}{5 25 + λ ^{2}}$ , so $25 + λ^{2} = 50$ and $λ = \pm 5$ .

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

⏱ 2mℹ️ Source: QB

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