On the \( x y \) plane where \( O \) is the origin, given points, \( A(1,0), B(0,1) \) and \( C(...

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On the \( x y \) plane where \( O \) is the origin, given points, \( A(1,0), B(0,1) \) and \( C(1,1) \). Let \( P, Q \) and \( R \) be moving point on the line \( O A, O B, O C \) respectively such that \( \mathrm{OP}=45 t(\mathrm{OA}), \mathrm{OQ}=60 t(\mathrm{OB}), \mathrm{OR}=(1-t)(\mathrm{OC}) \) with \( t0 \). If the three points \( P, Q \) and \( R \) are collinear, then the value of \( t \) is equal to
(a) \( \frac{1}{106} \)
(b) \( \frac{7}{187} \)
(c) \( \frac{1}{100} \)
(d) None of these
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