Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, 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
−32
cos(P+Q)+cos(Q+R)+cos(R+P)=−(cos R+cos P+cos Q)Max. of cos P+cos Q+cos R=32Min. of cos(P+Q)+cos(Q+R)+cos(R+P)=−32