Prove that the bus stop (S) is the closest point to Rajpur (R) on the Clock Tower to IMA(I) Road.

The vector from Rajpur (R) to Bus Stop (S) is: $\vec{RS} = \vec{OS} - \vec{OR} = (2\hat{i} + 6\hat{j}) - (8\hat{i} + 4\hat{j}) = -6\hat{i} + 2\hat{j}$. The line from Clock Tower to IMA is in the direction of $\vec{OI} = 3\hat{i} + 9\hat{j}$ (or $\vec{OS} = 2\hat{i} + 6\hat{j}$). Taking the dot product of $\vec{RS}$ with $\vec{OI}$: $\vec{RS} \cdot \vec{OI} = (-6)(3) + (2)(9) = -18 + 18 = 0$. Since $\vec{RS}$ is perpendicular to the line joining Clock Tower and IMA, S is the foot of the perpendicular from R to that line. Therefore, S is the closest point to Rajpur on the Clock Tower to IMA road.