The co-ordinates of the point where the line 2 x − 1 = − 3 y − 2 = 4 z + 3 meet the plane 2 x + 4 y − z = 1 are

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryMiscellaneous/MixedEasy2 minPYQ_2020

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The co-ordinates of the point where the line $\frac{x - 1}{2} = \frac{y - 2}{- 3} = \frac{z + 3}{4}$ meet the plane $2 x + 4 y - z = 1$ are

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(A) Let $\frac{x - 1}{2} = \frac{y - 2}{- 3} = \frac{z + 3}{4} = λ$ and $P$ be any point on the given line. $∴ P = (2 λ + 1, - 3 λ + 2, 4 λ - 3)$ Since point $P$ lies on the plane, we write $2 (2 λ + 1) + 4 (- 3 λ + 2) - (4 λ - 3) = 1$ $4 λ + 2 + 8 - 12 λ - 4 λ + 3 = 1 \Rightarrow λ = 1$ $∴ P \equiv (3, - 1, 1)$

Stream:MHT_CETSubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2020

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