The sum of the magnitudes of two 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 are the magnitudes of forces?

Explanation

Let (A) and (B) be two forces acting at a point and ` theta` be the angle between them. Then
`A+B =18 ` …(i)
and ` A^2 + B^2 +2 AB cos theta = 12^2 = 144` ….(ii)
If (A) si smaller force thea as per question
` tan 90^2 = (B sin theta)/(A+B cos theta)` or ` prop = (B sin theta)/(A+B cos theta)`
or ` A+B cos theta =0 ` or ` cos theta =- A//B`
` From (ii) , ` A^2 -B^2 + 2 AB (- A//B) = 144`
or ` B^2 - A^2 = 144`
or` (B-A(B+A) = 144`
or `B- A = (144)/(B+A) = (144)/(18) = 8 `...(iii)
Sloving (i) and (iii), we shall get , ` A= 5 N`.