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Let O be the origin and vec(OX) , vec(O...

Let O be the origin and` vec(OX) , vec(OY) , vec(OZ)` be three unit vector in the directions of the sides `vec(QR) , vec(RP),vec(PQ)` respectively , of a triangle PQR.
if the triangle PQR varies , then the manimum value of `cos (P+Q) + cos(Q+R)+ cos (R+P)` is

A

`-(3)/(2)`

B

`(3)/(2)`

C

`(5)/(3)`

D

`-(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
cos (P+Q) + cos(Q +R) + cos (R+P)
=- (cos R + cos P + cos Q)
Max . Of cos `P + cos Q + cos (Q +R) =(3)/(2)`
Min. of cos (P+Q) cos (Q+R) + cos (R+P) is `=-(3)/(2)`
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