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Question

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)
=cosRcosPcosQ=(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

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