How to find centroid/ orthogonal using vectors?

Question

The answer to this question is option D in my textbook but I think all the options are correct. This question was asked in IIT ADV 2017.

Answer 1

If you manipulate the algebra, you'll find that $$\overrightarrow{PS}\cdot\overrightarrow{RQ} = \overrightarrow{QS}\cdot\overrightarrow{PR}= \overrightarrow{RS}\cdot\overrightarrow{PQ}= 0.$$ This tells us that $S$ is the intersection of the altitudes of $\triangle PQR$.