Show that, if three forces acting on a particle can be taken sequentially to form the three sides of a triangle, theirresultant is zero.

Show that, if three forces acting on a particle can be taken sequentia

1.	Show that, if three forces acting on a particle can be taken sequentially to form the three sides of a triangle, theirresultant is zero.
Answer» Solution :Let `veca , vecb and vecc` be the three forces acting at a point O [Fig.2.73 (a)].Now, TAKING these forces sequentially and KEEPING their magnitudesand directionsthe same, we obtain the three sides of a triangle, `vec(PQ) , vec(QR) and vec(RP)` [Fig.2.73(b)]. We have to show that `veca+vecb+vecc=vec0` According to the triangle LAW of vector addition, `veca+vecb=vec(PR)=-vec(RP) or, veca+vecb=-vecc` or, `veca+vecb+vecc=vec0` `therefore` The resultant of the forces `veca,vecb and vecc` is ZERO.