1) Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR,RP,PQ respectively of triangle PQR. I f the triangle PQR varies, then the minimum value of $\cos(P+Q)+\cos(Q+R)+\cos(R+P)$ is A) $-\frac{3}{2}$ B) $\frac{3}{2}$ C) $\frac{5}{3}$ D) $-\frac{5}{3}$ Answer: Option AExplanation:$\cos(P+Q)+\cos(Q+R)+\cos(R+P)=-(cosR+\cos P+\cos Q)$ Max of $\cos P+\cos Q +\cos R=\frac{3}{2}$ Min of $\cos(P+Q)+\cos(Q+R)+\cos(R+P) is =-\frac{3}{2}$
