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

If two vectors are perpendicular then their dot product must be equal to zero. Let say two vectors are A→ and B→ . According to problem A→+B→ is perpendicular to A→-B→.∴A→+B→⋅A→−B→=0⇒A→⋅A→−A→⋅B→+B→⋅A→−B→⋅B→=0⇒A2−B2=0⇒A2=B2∴ A = B i.e., two vectors are equal to each other in magnitude.