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

Options

A. parallel to each other
B. perpendicular to each other
C. equal in magnitude
D. unequal in magnitude

Answer

C

Explanation

Let `vec P and vec Q` be the two forces.
Then, `vec R = vec P + vec Q and vec R = vec P - vec Q`
It is given that `vec R bot vec R" "therefore vec R cdot vec R=0`
`therefore vec P cdot vec P - vec P cdot vec Q+vec Q cdot vec P - vec Q cdot vec Q=0`
`(because vec P cdot vec Q = vec Q cdot vec P)`
`therefore P^(2) -Q^(2)=0" "therefore P^(2) =Q^(2)`
`vec P = pm Q" or "|P|=|Q|`
`therefore` The two forces are equal in magnitude.