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

Explanation

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 magnitudes and directions the 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.