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)
A
−53
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B
−32
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C
32
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D
53
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Solution
The correct option is B−32
cos(P+Q)+cos(Q+R)+cos(R+P) =−cosR−cosP−cosQ=−(cosR+cosP+cosQ) In any triangle, the maximum value of cosP+cosQ+cosR=32 ∴ Minimum value of the given expression cos(P+Q)+cos(Q+R)+cos(R+P)=−32