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Question
Consider three points P=[−sin(β−α),−cosβ],Q=[cos(β−α),sinβ] and R=[cos(β−α+θ),sin(β−θ)], where 0<α,β,θ<π4. Then
Consider three points P=[−sin(β−α),−cosβ],Q=[cos(β−α),sinβ] and R=[cos(β−α+θ),sin(β−θ)], where 0<α,β,θ<π4. Then
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Solution
The correct option is D P, Q, R are non-collinear
Given,Points P(−sin(β−α),−cosβ),Q(cos(β−α),sinβ) and R(cos(β−α+θ),sin(β−θ))
we get,
Slope of line joining PQ m1=sinβ+cosβcos(β−α)+sin(β−α).........................................(1)
Slope of line joining QR m2=sin(β−θ)−sinβcos(β−α+θ)−cos(β−α)=cos(β−θ2)sin(β−α+θ2)..................................(2)
From (1) and (2),
we get m1≠m2
∴P,Q,R are not collinear.
Given,Points P(−sin(β−α),−cosβ),Q(cos(β−α),sinβ) and R(cos(β−α+θ),sin(β−θ))
we get,
Slope of line joining PQ m1=sinβ+cosβcos(β−α)+sin(β−α).........................................(1)
Slope of line joining QR m2=sin(β−θ)−sinβcos(β−α+θ)−cos(β−α)=cos(β−θ2)sin(β−α+θ2)..................................(2)
From (1) and (2),
we get m1≠m2
∴P,Q,R are not collinear.
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