Direction cosines of the line x + 2 2 = 2 y - 5 3 , z = - 1 are _______

Any line contained in a plane is perpendicular to the normal of the plane ⇒ The direction ratios of given line x + 2 2 = 2 y − 5 3 ⇔ 3 x − 4 y + 16 = 0 , z = − 1 ⇔ z + 1 = 0 i ^ j ^ k ^ 3 4 0 0 0 1 = 4 i ^ - 3 j ^ ⇒ direction cosines are ± ( 4 5 , 3 5 , 0 )

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2016

MathematicsEasysingle choice

Direction cosines of the line $\frac{x + 2}{2} = \frac{2 y - 5}{3}, z = - 1$ are _______

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Answer:

Solution:

Any line contained in a plane is perpendicular to the normal of the plane
$\Rightarrow$ The direction ratios of given line
$\frac{x + 2}{2} = \frac{2 y - 5}{3} \Leftrightarrow 3 x - 4 y + 16 = 0,$
$z = - 1 \Leftrightarrow z + 1 = 0$
$|\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 4 & 0 \\ 0 & 0 & 1 \end{matrix}| = 4 \hat{i} - 3 \hat{j}$
$\Rightarrow$ direction cosines are $\pm (\frac{4}{5}, \frac{3}{5}, 0)$

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

⏱ 2mℹ️ Source: PYQ_2016

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