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Question

Let $O$ be the origin and $\overrightarrow{OX}$, $\overrightarrow{OY}$, $\overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR}$, $\overrightarrow{RP}$, $\overrightarrow{PQ}$ respectively, of a triangle $PQR$. If the triangle $PQR$ varies, then the minimum value of $\cos(P + Q) + \cos(Q + R) + \cos(R + P)$ is:

$-\frac{5}{3}$

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

Solution

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