Consider three points `P = (-sin (beta-alpha), -cos beta)`, `Q = (cos(beta-alpha), sin beta)`, and `R = ((cos (beta - alpha + theta), sin (beta - theta))`, where `0< alpha, beta, theta < pi/4` Then

Options

A. P lies on the line segment RQ
B. Q lies on the segment PR
C. R lies on the line segment PR
D. P,Q,R are non-collinear

Explanation

To find the relationship between the points P, Q, and R, we will follow these steps:

### Step 1: Define the Points
We have three points defined as follows:
- \( P = (-\sin(\beta - \alpha), -\cos(\beta)) \)
- \( Q = (\cos(\beta - \alpha), \sin(\beta)) \)
- \( R = (\cos(\beta - \alpha + \theta), \sin(\beta - \theta)) \)

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