The ratio in which the plane r ˉ . ( i ^ − 2 j ^ + 3 k ^ ) = 17 divides the line joining the points − 2 i ^ + 4 j ^ + 7 k ^ and 3 i ^ − 5 j ^ + 8 k ^

Let the required ratio be λ : 1 then the point of division lies on the plane. λ + 1 3 λ − 2 − 2 x λ + 1 − 5 λ + 4 + 3 × λ + 1 8 λ + 7 = 17 ⇒ λ = 10 3 The required ratio is 3 : 10

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

Mathematics3D-Coordinate GeometryMiscellaneous/MixedMedium2 minPYQ_2022

MathematicsMediumsingle choice

The ratio in which the plane $\overset{r}{ˉ}$ . $(\hat{i} - 2 \hat{j} + 3 \hat{k}) = 17$ divides the line joining the points $- 2 \hat{i} + 4 \hat{j} + 7 \hat{k}$ and $3 \hat{i} - 5 \hat{j} + 8 \hat{k}$

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Let the required ratio be $λ : 1$ then the point of division lies on the plane. $\frac{3 λ - 2}{λ + 1} - 2 x \frac{- 5 λ + 4}{λ + 1} + 3 \times \frac{8 λ + 7}{λ + 1} = 17 \Rightarrow λ = \frac{3}{10}$ The required ratio is $3 : 10$

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

⏱ 2mℹ️ Source: PYQ_2022

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