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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) is


A

32

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B

32

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C

53

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D

53

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Solution

The correct option is A

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


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