The direction cosines ℓ , m , n of the line 2 x + 2 = 3 2 y − 4 ; z = − 1

We have line 2 x + 2 = 3 2 y − 5 , z = − 1 i.e. 2 x − ( − 2 ) = 3 2 ( y − 2 5 ) , z = − 1 i.e. 2 x − ( − 2 ) = ( 2 3 ) ( y − 2 5 ) , z = − 1 Here direction ratios are 2 , 2 3 Also ( 2 ) 2 + ( 2 3 ) 2 + 0 = ± 2 5 Here required direction cosines are ( ± 2 5 ) 2 , ( ± 2 5 ) ( 2 3 ) , ( ± 2 5 ) 0 i.e. ± 5 4 , ± 5 3 , 0

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2021

MathematicsEasysingle choice

The direction cosines $ℓ, m, n$ of the line $\frac{x + 2}{2} = \frac{2 y - 4}{3}; z = - 1$

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Answer:

Solution:

We have line $\frac{x + 2}{2} = \frac{2 y - 5}{3}, z = - 1$ i.e. $\frac{x - ( - 2 )}{2} = \frac{2 ( y - \frac{5}{2} )}{3}, z = - 1$ i.e. $\frac{x - ( - 2 )}{2} = \frac{( y - \frac{5}{2} )}{( \frac{3}{2} )}, z = - 1$ Here direction ratios are $2, \frac{3}{2}$ Also $(2)^{2} + (\frac{3}{2})^{2} + 0 = \pm \frac{5}{2}$ Here required direction cosines are $\frac{2}{( \pm \frac{5}{2} )}, \frac{( \frac{3}{2} )}{( \pm \frac{5}{2} )}, \frac{0}{( \pm \frac{5}{2} )} i.e. \pm \frac{4}{5}, \pm \frac{3}{5}, 0$

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

⏱ 2mℹ️ Source: PYQ_2021

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