Show that if theree forces are represented by the three medians of a triangle, they will be in equilibrium.

Explanation

Let the medians of the `Delta ABC` be AD,BE, and CF. vectors `vec(AD),vec(BE) and vec(CF)` represent the three forces [Fig.2.16]. We have to show :`vec(AD)+vec(BE)+vec(CF)=vec(0).`
As per triangle law of vector addition,

`vec(AD)=vec(AC)+vec(CD)=vec(AC)+1/2vec(CB)`
`vec(BE)=vec(BA)+vec(AE)=vec(BA)+1/2vec(AC)`
`vec(CF)=vec(CB)+vec(BF)=vec(CB)+1/2vec(BA)`
Hence, `vec(AD)+vec(BE)+vec(CF)=3/2(vec(AC)+vec(CB)+vec(BA))=vec(0)`
[as sum of 3 vectors, represented by the 3 sides of a triangle taken in order, is zero].