JEE Advanced 2017 Paper 2 Mathematics Q16

Mathematics

Problem

Read the following paragraph and answer Q.15 and Q.16. Let OO be the origin, and OX→,OY→,OZ→\overrightarrow{OX},\overrightarrow{OY},\overrightarrow{OZ} be three unit vectors in the directions of the sides QR→,RP→,PQ→\overrightarrow{QR},\overrightarrow{RP},\overrightarrow{PQ}, respectively, of a triangle PQRPQR. If the triangle PQRPQR varies, then the minimum value of cos⁡(P+Q)+cos⁡(Q+R)+cos⁡(R+P)\cos(P+Q)+\cos(Q+R)+\cos(R+P) is

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