CUET Preparation Today
CUET
-- Mathematics - Section B1
Vectors
Let O be the origin, and →OX,→OY,→OZ be three unit vectors in the directions of the sides →QR,→RP,→PQ respectively, of a triangle PQR. Then, |→OX×→OY|=
sin(P+Q)
sin2R
sin(P+R)
sin(Q+R)
|→OX×→OY|
=|→OX||→OY|sin(π−R)
=sinR=sin(π−(P+Q))=sin(P+Q) [∵P+Q+R=π]
