Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that $$\overrightarrow { O P } \cdot \overrightarrow { O Q } + \overrightarrow { O R } \cdot \overrightarrow { O S } = \overrightarrow { O R } \cdot \overrightarrow { O P } + \overrightarrow { O Q } \cdot \overrightarrow { O S } = \overrightarrow { O Q } \cdot \overrightarrow { O R } + \overrightarrow { O P } \cdot \overrightarrow { O S }$$ Then the triangle $P Q R$ has $S$ as its [A] centroid [B] circumcentre [C] incentre [D] orthocenter
Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that
$$\overrightarrow { O P } \cdot \overrightarrow { O Q } + \overrightarrow { O R } \cdot \overrightarrow { O S } = \overrightarrow { O R } \cdot \overrightarrow { O P } + \overrightarrow { O Q } \cdot \overrightarrow { O S } = \overrightarrow { O Q } \cdot \overrightarrow { O R } + \overrightarrow { O P } \cdot \overrightarrow { O S }$$
Then the triangle $P Q R$ has $S$ as its
[A] centroid
[B] circumcentre
[C] incentre
[D] orthocenter