Two forces ` vec A B` and ` vec A D` are acting at vertex A of a quadrilateral ABCD and two forces ` vec C B` and ` vec C D` at C prove that their resultant is given by 4` vec E F` , where E and F are the midpoints of AC and BD, respectively.

Explanation

`vec(AB)+vec(AD)=2vec(AF)`, where F is the midpoint of BD.
`" "vec(CB)+vec(CD)=2vec(CF)`
`therefore" "vec(AB)+vec(AD)+vec(CB)+vec(CD)=2(vec(AF)+vec(CF))`
`" "=-2(vec(FA)+vec(FC))`
`" "=-2[2vec(FE)]`, where E is the midpoint of AC
`" "=4vec(EF)`