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Consider three points $P (\cos α, \sin β),$ $Q (\sin α, \cos β)$ and $R (0, 0) .$ Where $0 < α, β < π / 4$ Then

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P lies on the line segment RQ

Q lies on the line segment PQ

R lies on the line segment QP

P, Q, R are non-collinear.

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detailed solution

Correct option is D

Consider Δ=cos⁡αsin⁡β1sin⁡αcos⁡β1001=cos⁡αcos⁡β−sin⁡αsin⁡β=cos⁡(α+β)≠0 as 0<α+β<π/2Hence the given points are non-collinear.

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Consider three points P(cos⁡α,sin⁡β), Q(sin⁡α,cos⁡β) and R(0,0). Where 0<α,β<π/4 Then

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Consider three points $P (\cos α, \sin β),$ $Q (\sin α, \cos β)$ and $R (0, 0) .$ Where $0 < α, β < π / 4$ Then