A line makes angles ∝ , β , γ with the co-ordinate axes, then cos 2 ∝ + cos 2 β + cos 2 γ is equal to

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2020

MathematicsMediumsingle choice

A line makes angles $\propto, β, γ$ with the co-ordinate axes, then $cos 2 \propto + cos 2 β + cos 2 γ$ is equal to

Answer:

Solution:

$cos 2 α + cos 2 β + cos 2 γ$ $= 2 cos^{2} α - 1 + 2 cos^{2} β - 1 + 2 cos^{2} γ - 1$ $= 2 (cos^{2} α + cos^{2} β + cos^{2} γ) - 3 = 2 (1) - 3 = - 1$

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

⏱ 2mℹ️ Source: PYQ_2020

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