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

`P + Q = 18 rArr 18 - P` (i)
`tan 90^(@) = (1)/(0) = (Q sin theta)/(P + Q cos theta)`
`P + Q cos theta = 0 rArr Q cos theta = -P` (ii)
`R^(2) = P^(2) + Q^(2) + 2 PQ cos theta`
`(12)^(2) = P^(2) + (18 - P)^(2) + 2P(-P)`
`144 = P^(2) + 324 + P^(2) - 36 P - 2P^(2)`
`36 P = 180 rArr P = 5 unit`
`Q = 18 - P = 13 unit`