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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryFamily of planesMedium2 minQB

MathematicsMediummultiple choice

The plane $l x + m y = 0$ is rotated about its line of intersection with the plane $z = 0$ through an angle $α$ . The equation of the plane in its new position may be

Options:(select one or more)

Answer:

A, B

Solution:

The required plane is $l x + m y + λ z = 0$ . The angle with $l x + m y = 0$ is $α : cos α =$ $\frac{l ^{2} + m ^{2}}{l ^{2} + m ^{2} l ^{2} + m ^{2} + λ ^{2}}$ , so $cos^{2} α = \frac{l ^{2} + m ^{2}}{l ^{2} + m ^{2} + λ ^{2}}$ and $λ = \pm l^{2} + m^{2} tan α$ .

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

⏱ 2mℹ️ Source: QB

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