Question

❥ Question :-

derive traingle law of vector
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Note :- no copied answers !​

Answer 1

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$\implies$Consider two vectors P and Q acting on a body and represented both in magnitude and direction by sides OA and AB respectively of a triangle OAB.

$\implies$Let θ be the angle between P and Q. Let R be the resultant of vectors P and Q.

Then, according to triangle law of vector addition, side OB represents the resultant of P and Q.

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Answer 2

Explanation:

Consider two vectors P⃗  and Q⃗  that are represented in the order of magnitude and direction by the sides OA and AB, respectively of the triangle OAB. Let R⃗ be the resultant of vectors P⃗  and Q⃗ .

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

Substituting the values of AC and BC in (eqn.1), we get

R2=(P+QcosΘ)2+(QsinΘ)2

R2=P2+2PQcosΘ+Q2co