Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryPlane (Equations)Easy2 minPYQ_2012

MathematicsEasysingle choice

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of $△ ABC$ is at the point $(1, 2, 3)$ , then equation of the plane is

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Solution:

Let the equation of the required plane be $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$ This meets the coordinate axes at $A, B$ and $C$ , the coordinates of the centroid of $△ ABC$ are $(\frac{a}{3}, \frac{b}{3}, \frac{c}{3})$ $∴ \frac{a}{3} = 1, \frac{b}{3} = 2, \frac{c}{3} = 3 \Rightarrow a = 3, b = 6, c = 9$ Hence, the equation of the plane is $\frac{x}{3} + \frac{y}{6} + \frac{z}{9} = 1$

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

⏱ 2mℹ️ Source: PYQ_2012

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