Consider three points P = ( − sin ( β − α ) , − cos β ) , Q = ( cos ( β − α ) , sin β ) and R = ( cos ( β − α + θ ) , sin ( β − θ ) , where 0

Question

Consider three points P = ( − sin ( β − α ) , − cos β ) , Q = ( cos ( β − α ) , sin β ) and R = ( cos ( β − α + θ ) , sin ( β − θ ) , where 0 < α , β , θ < 4 π ​ . Then,

TestHub · Accepted Answer

For collinear points Δ = ​ − sin ( β − α ) cos ( β − α ) cos ( β − α + θ ) ​ − cos β sin β sin ( β − θ ) ​ 1 1 1 ​ ​ Clearly, Δ  = 0 for any value of α , β , θ , hence points are non-collinear.

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JEE Advanced (2028)