The angle between two lines 2 x + 1 = 2 y + 3 = − 1 z − 4 and 1 x − 4 = 2 y + 4 = 2 z + 1 is

The required angle θ = cos − 1 ( 2 2 + 2 2 + 1 2 ⋅ 1 2 + 2 2 + 2 2 2 × 1 + 2 × 2 + ( − 1 ) × 2 ) ⇒ θ = cos − 1 ( 3 × 3 4 ) ⇒ θ = cos − 1 ( 9 4 )

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2022

MathematicsMediumsingle choice

The angle between two lines $\frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{- 1}$ and $\frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2}$ is

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The required angle $θ = cos^{- 1} (\frac{2 \times 1 + 2 \times 2 + ( - 1 ) \times 2}{2 ^{2} + 2 ^{2} + 1 ^{2} \cdot 1 ^{2} + 2 ^{2} + 2 ^{2}}) \Rightarrow θ = cos^{- 1} (\frac{4}{3 \times 3}) \Rightarrow θ = cos^{- 1} (\frac{4}{9})$

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

⏱ 2mℹ️ Source: PYQ_2022

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