The angle between the line 2 x − 1 = 1 y + 3 = 2 z + 7 and the plane r ˉ ⋅ ( 6  ^ − 2  ^ − 3 k ^ ) = 5 is

Angle between line and plane is given by sin θ = a 2 + b 2 + c 2 a 1 2 + b 1 2 + c 1 2 a a 1 + b b 1 + c c 1 Here a = 2 , b = 1 , c = 2 and a 1 = 6 , b 1 = − 2 , c 1 = − 3 ∴ sin θ = 3 × 7 12 − 2 − 6 = 21 4 ⇒ θ = sin − 1 ( 21 4 )

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

Mathematics3D-Coordinate GeometryMiscellaneous/MixedEasy2 minPYQ_2020

MathematicsEasysingle choice

The angle between the line $\frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2}$ and the plane $\overset{r}{ˉ} \cdot (6 \overset{}{^} - 2 \overset{}{^} - 3 \hat{k}) = 5$ is

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Angle between line and plane is given by $sin θ = \frac{a a _{1} + b b _{1} + c c _{1}}{a ^{2} + b ^{2} + c ^{2} a _{1}^{2} + b _{1}^{2} + c _{1}^{2}}$ Here $a = 2, b = 1, c = 2$ and $a_{1} = 6, b_{1} = - 2, c_{1} = - 3$ $∴ sin θ = \frac{12 - 2 - 6}{3 \times 7} = \frac{4}{21} \Rightarrow θ = sin^{- 1} (\frac{4}{21})$

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

⏱ 2mℹ️ Source: PYQ_2020

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