The sum of magnitudes of two forces acting at a point is 16N. If their resultant is normal to the smaller force and has a magnitude of 8N. Then the forces are

Explanation

Let `vec(F)` be the resultant of two forces `vec(F)_(1)` and `vec(F)_(2)` as shown in figure with `F_(2) gt F_(1)`.
`F_(2) sin theta = F_(1)` ….(i)
`F_(2) cos theta = F = 8` …..(ii)
Squaring and adding Eqs (i) and (ii), we get
`F_(2)^(2) = F_(1)^(2) + 64` .....(iii)
Given `F_(1) + F_(2) = 16` .....(iv)
Solving Eqs. (iii) and (iv), we get
`F_(1) = 6N` and `F_(2) = 10 N`