Question

Give analytical treatment of triangle vector addition and theme find the direction of the resultant vector

Answer 1

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,
             
              

Answer 2

Triangle Law of Vector Addition

Statement of Triangle Law

If 2 vectors acting simultaneously on a body are represented both in magnitude and direction by 2 sides of a triangle taken in an order then the resultant(both magnitude and direction) of these vectors is given by 3rd side of that triangle taken in opposite order.