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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2011

MathematicsMediumsingle choice

If $α, β$ and $γ$ are the angles which a half ray makes with the positive direction of the axes, then $sin^{2} α + sin^{2} β + sin^{2} γ$ is equal to

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Answer:

Solution:

Given expression, $sin^{2} α + sin^{2} β + sin^{2} γ$ $= (1 - cos^{2} α) + (1 - cos^{2} β) + (1 - cos^{2} γ) = 3 - cos^{2} α + cos^{2} β + cos^{2} γ = 3 - 1 = 2 (∵ cos^{2} α + cos^{2} β + cos^{2} γ = 1)$

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

⏱ 2mℹ️ Source: PYQ_2011

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