WBJEE · Maths · Straight Lines
Consider three points \(P(\cos \alpha, \sin \beta), Q(\sin \alpha, \cos \beta), R(0,0)\), where \(0 \lt \alpha, \beta \lt \frac{\pi}{4}\). Then
- A \(P\) lies on the line segment RQ
- B Q lies on the line segment PR
- C \(R\) lies on the line segment \(P Q\)
- D P, Q, R are non-collinear
Answer & Solution
Correct Answer
(D) P, Q, R are non-collinear
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Consider } \Delta=\left|\begin{array}{ccc} \cos \alpha & \sin \beta & 1 \\ \sin \alpha & \cos \beta & 1 \\ 0 & 0 & 1 \end{array}\right| \\ & =\cos \alpha \cos \beta-\sin \alpha \sin \beta \\ & =\cos (\alpha+\beta) \neq 0 \text { as } 0 < \alpha+\beta <…
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