The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

Options

A. are equal to each other
B. are not equal to each other in magnitude
C. cannot be predicted
D. are equal to each other in magnitude

Answer

D

Explanation

Let `vec P and vec Q` be the two forces `(P gt Q) and vec R_(1)=vec P + vec Q and vec R_(2) = vec P - vec Q`
If `vec R_(1) bot vec R_(2)" then "vec R_(1) cdot vec R_(2)=0`
`therefore (vec P + vec Q) cdot (vec P - vec Q)=0`
`therefore P^(2) -PQ+PQ-Q^(2) =0`
`therefore P^(2) =Q^(2)" or "|P|=|Q|`
Thus the magnitudes of the two forces are equal.