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

Options

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

Answer

A

Explanation

Let `vec(F_(1))` and `vec(F_(2))` br the two forces. Then
`vec(F_(s))=vec(F_(1)) + vec(F_(2))` and `vec(F_(d))=vec(F_(1))-vec(F_(2))`
Now `vec(F_(s))` is `bot`r to `vec(F_(d)):.vec(F_(s)).vec(F_(d))=0`
or `|vec(F_(1))|^(2)=|vec(F_(2))|^(2)` or `|vec(F_(1))|=|vec(F_(2))|`
The forces are equal in magnitude.