Paragraph: Let $O$ be the origin, and $\overrightarrow{O X}, \overrightarrow{O Y}, \overrightarrow{O Z}$ be three unit vectors in the directions of the sides $\overrightarrow{Q R}, \overrightarrow{R P}$, $\overrightarrow{P Q}$, respectively, of a triangle $P Q R$.
Question: If the triangle $P Q R$ varies, then the minimum value of $\cos (P+Q)+\cos (Q+R)+\cos (R+P)$ is

• Correct answer
  A

  $-\frac{3}{2}$
• B

  $\frac{3}{2}$
• C

  $\frac{5}{3}$
• D

  $-\frac{5}{3}$

Hence, the correct answer is option: 'A'.