Question

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

Answer 1

Answer:

Consider two vectors P and Q that are represented in the order of magnitude and direction by the sides OA and AB respectively of the triangle OAB. ... To determine the direction of the resultant vector, let ɸ be the angle between the resultant vector R and P.

Answer 2

Answer:

Explanation:

Triangle Law of Vector Addition Derivation

Consider two vectors P and Q that are represented in the order of magnitude and direction by the sides OA and AB respectively of the triangle OAB. Let R be the resultant of vectors P and Q

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=ACAB AC=ABcosΘ=QcosΘ sinΘ=BCAB 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.

To determine the direction of the resultant vector, let ɸ be the angle between the resultant vector R and P.

From triangle OBC,

tanϕ=BCOC=BCOA+AC tanϕ=QsinΘP+QcosΘ

therefore, ϕ=tan−1(QsinΘP+QcosΘ)

Above equation is the direction of the resultant vecto