Let O be the origin, and OX, OY , OZ be three unit vectors in the directions of the sides

Question

Let O be the origin, and \(\vec{OX},\vec{OY},\vec{OZ}\) be three unit vectors in the directions of the sides \(\vec{OR},\vec{RP},\vec{PQ}\) respectively, of a triangle PQR.

1. \(|\vec{OX}\times \vec{OY}|\)

(A) sin (P+Q)

(B) sin 2R

(C) sin(P + R)

(D) sin(Q + R)

2. If the triangle PQR varies, then the minimum value of

cos(P + Q)+cos(Q + R) +cos(R+P)

(A) -5/3

(B) -3/2

(C) 3/2

(D) 5/3

Answer 1

(1) (A) sin (P+Q)

(2) (B) -3/2