Find the position vector of the bus stop (S) relative to the Clock Tower.

Clock Tower is the origin O $(0, 0)$. Position vector of IMA (I) relative to O: $\vec{OI} = 3\hat{i} + 9\hat{j}$. Position vector of Rajpur (R): $\vec{OR} = \vec{OI} + (5\hat{i} - 5\hat{j}) = (3+5)\hat{i} + (9-5)\hat{j} = 8\hat{i} + 4\hat{j}$. Since the bus stop S is two thirds of the way along the road from Clock Tower to IMA: $\vec{OS} = \frac{2}{3}\vec{OI} = \frac{2}{3}(3\hat{i} + 9\hat{j}) = 2\hat{i} + 6\hat{j}$.