Paragraph: Let O be the origin, and OX , O Y , OZ be three unit vectors in the directions of the sides QR , RP , PQ , respectively, of a triangle PQR . Question: If the triangle PQR varies, then t

Question

Paragraph: Let O be the origin, and OX , O Y , OZ be three unit vectors in the directions of the sides QR ​ , RP , PQ ​ , respectively, of a triangle PQR . Question: If the triangle PQR varies, then the minimum value of cos ( P + Q ) + cos ( Q + R ) + cos ( R + P ) is

TestHub · Accepted Answer

cos P + Q + cos Q + R + cos R + P = cos 180 − R + cos 180 − P + cos 180 − Q = − cos P + cos Q + cos R In any Δ P Q R , cos P + cos Q + cos R ≤ 3 2 ⇒ − cos P + cos Q + cos R ≥ − 3 2

Mathematics - Properties of Triangles Question with Solution | TestHub

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