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 equal to each other

Answer

A

Explanation

If two vector are perpendicular then their dot product must be equal to zero. According to problem
`(vec(A)+vec(B)).(vec(A)-vec(B))= 0 implies vec(A).vec(A)-vec(A).vec(B)+vec(B).vec(A)-vec(B).vec(B)=0`
`implies A^(2)-B^(2)= 0 implies A^(2)= B^(2)`
i.e., two vector are equal to each other in magnitude.