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Let O be the origin, and O X x O Y ,...

Let `O` be the origin, and ` O X x O Y , O Z ` be three unit vectors in the direction of the sides ` Q R ` , ` R P ` , ` P Q ` , 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

`-(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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