The mirror image of the point ( 1 , 2 , 3 ) in a plane is ( − 3 7 , − 3 4 , − 3 1 ) . Thus, the point lies on this plane.

M is the midpoint. ∴ M ≡ ( − 3 2 , 3 1 , 3 4 ) D.r.s of AB are 3 − 10 , 3 − 10 , 3 − 10 i.e., 1 , 1 , 1 Equation of plane is 1 ( x + 3 2 ) + 1 ( y − 3 1 ) + 1 ( z − 3 4 ) = 0 ⇒ x + y + z = 1 Option (A) satisfies this equation of the plane.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2023

MathematicsEasysingle choice

The mirror image of the point $(1, 2, 3)$ in a plane is $(- \frac{7}{3}, - \frac{4}{3}, - \frac{1}{3})$ . Thus, the point lies on this plane.

Options:

Answer:

Solution:

$M$ is the midpoint. $∴ M \equiv (- \frac{2}{3}, \frac{1}{3}, \frac{4}{3})$ D.r.s of $AB$ are $\frac{- 10}{3}, \frac{- 10}{3}, \frac{- 10}{3}$ i.e., $1, 1, 1$ Equation of plane is $1 (x + \frac{2}{3}) + 1 (y - \frac{1}{3}) + 1 (z - \frac{4}{3}) = 0 \Rightarrow x + y + z = 1$ Option (A) satisfies this equation of the plane.

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2023

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