The sum of the magnitudes of wto forces acting at a point is 18 and the magnitude of their resultant is 12 If the resultant is at `90^(@)` with the force of smaller magnitude , what aarae the magnitude of fores ?

Explanation

Let P be the smaller force and Q be the greater force. Then
`P+Q=18`..(i)
`R=sqrt(P^(2)+Q^(2)+2PQ cos theta)=12`...(ii)
`tan phi =(Qsin theta)/(P+Qcos theta)=tan90=oo`
`:. P+Q cos theta=0`..(iii)
By solving (i),(ii),and (iii),we will get P=5 and Q=13.