Question

Drawing the necessary figure, explain the method of triangle for the addition of vector.​

Answer 1

Derivation of the law
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. 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.



So, we have

R = P + Q

Now, expand A to C and draw BC perpendicular to OC.

From triangle OCB,



In triangle ACB,



Also,



Magnitude of resultant:

Substituting value of AC and BC in (i), we get



which is the magnitude of resultant.

Direction of resultant: Let ø be the angle made by resultant R with P. Then,

From triangle OBC,



which is the direction of resultant.

Answer 2

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