Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryPerpendicular distance of a point from a planeMedium2 minQB

MathematicsMediumsingle choice

If the perpendicular distance of a point P other than the origin from the plane $x + y + z = p$ is equal to the distance of the plane from the origin, then the coordinates of P are

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Solution:

The distance of the origin from the plane is $\frac{∣ p ∣}{3}$ . For $P (x, y, z)$ we need $\frac{∣ x + y + z - p ∣}{3} = \frac{∣ p ∣}{3}$ , i.e. $∣ x + y + z - p ∣ = ∣ p ∣$ . This is satisfied by ( $2 p, p, - p$ ).

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Perpendicular distance of a point from a plane

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