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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: `-3/2` (b) `5/3` (c) `3/2` (d) `-5/3`

A

`-(5)/(3)`

B

`-(3)/(2)`

C

`(3)/(2)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`-(cosP+cosQ+cosR)`
`= vec(OX).vec(OY)+vec(OZ)+vec(OZ).vec(OX)`
`=((vec(OX)+vec(OY)+vec(OZ))^(2)-(|vec(OX)|^(2)+|vec(OY)|^(2)+|vec(OZ)|^(2)))/(2) ge-(3)/(2)`
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