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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryPlane (Equations)Medium2 minPYQ_2021

MathematicsMediumsingle choice

If a plane meets the axes $X, Y, Z$ in $A, B, C$ respectively such that centroid of $△ ABC$ is $(1, 2, 3)$ , then the equation of the plane is

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Answer:

Solution:

Let $A = (x, 0, 0); B = (0, y, 0); C = (0, 0, z)$ Centroid of $△ A BC$ is $(1, 2, 3)$ $∴ \frac{x}{3} = 1, \frac{y}{3} = 2, \frac{z}{3} = 3 \Rightarrow (x, y, z) = (3, 6, 9)$ Hence equation of required plane is $\frac{x}{3} + \frac{y}{6} + \frac{z}{9} = 1$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Plane (Equations)

⏱ 2mℹ️ Source: PYQ_2021

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