We have P ≡ (- sin (β - α) , - cos β) Q = (cos (β - α) , sin β) R = (cos (β - α + θ) = (x2cosθ+x1sinθ),(y2cosθ+y1sinθ) Let T is a point on PQ which divides PQ in cos θ: sin θ. Therefore, T =
(
x2cosθ+x1sinθ
cosθ+sinθ
,
y2cosθ+y1sinθ
cosθ+sinθ
)
Hence, P, Q and T are collinear and hence P, Q and R are non- collinear.