Question

derive expression for magnitude of resultant of two vectors using triangle law of vector addition​

Answer 1

R= P+ Q

From triangle OCB,

OB2=OC2+BC2 OB2

=(OA+AC)2+BC2 (eq.1)

In triangle ACB with ϴ as the angle between P and Q

cosΘ=AC/AB

AC=ABcosΘ=QcosΘ

sinΘ=BC/AB

BC=ABsinΘ=QsinΘ

R2=(P+QcosΘ)2+(QsinΘ)2 (after substituting AC and BC in eq.1)

R2=P2+2PQcosΘ+Q2cos2Θ+Q2sin2Θ R2=P2+2PQcosΘ+Q2

therefore, R=P2+2PQcosΘ+Q2−−−−−−−−−−−−−−−−−√

Above equation is the magnitude of the resultant vector.