The vector sum of two forces A and B is perpendicular to their vector difference. Hence forces A and B are

Step-by-step solution

The condition that the vector sum A + B is perpendicular to the vector difference A - B implies their dot product vanishes: ( A + B ) ( A - B ) = 0 Expanding using the distributive property yields: A A - A B + B A - B B = 0 Since dot product is commutative, A B = B A , causing the cross terms to cancel, leaving: | A |^2 - | B |^2 = 0 Thus | A |^2 = | B |^2 , and since magnitudes are non-negative, | A | = | B | . D