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JEE Advanced 2008Paper 2
Exam
JEE Advanced
Year
2008
Paper
Paper 2
Subject
Mathematics
Chapter
Straight Lines

JEE Advanced 2008 · Paper 2 · Mathematics · Straight Lines

Consider three points P=(- (β-α),- β), Q=( (β-α), β) and R=(...

Consider three points P=(−sin⁡(β−α),−cos⁡β),Q=(cos⁡(β−α),sin⁡β)P=(-\sin (\beta-\alpha),-\cos \beta), Q=(\cos (\beta-\alpha), \sin \beta) and R=(cos⁡(β−α+θ),sin⁡(β−θ)R=(\cos (\beta-\alpha+\theta), \sin (\beta-\theta), where 0<α,β,θ<π40 < \alpha, \beta, \theta < \frac{\pi}{4}. Then,

Options

  1. APP lies on the line segment RQR Q
  2. BQQ lies on the line segment PRP R
  3. CRR lies on the line segment QPQ P
  4. DP,Q,RP, Q, R are non- collinear

Correct answer

D. P,Q,RP, Q, R are non- collinear

Step-by-step solution

For collinear points \Delta=\left|−sin⁡(β−α)−cos⁡β1cos⁡(β−α)sin⁡β1cos⁡(β−α+θ)sin⁡(β−θ)1\begin{array}{ccc} -\sin (\beta-\alpha)& -\cos \beta& 1 \\ \cos (\beta-\alpha)& \sin \beta& 1 \\ \cos (\beta-\alpha+\theta)& \sin (\beta-\theta)& 1 \end{array}\right| Clearly,\Delta \neq 0foranyvalueoffor any value of\alpha, \beta, \theta$, hence points are non-collinear.
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