If for two vector A→ and B→, sum (A→+B→) is perpendicular to the difference (A→−B→). The ratio of their magnitude is

(A→+B→) is perpendicular to (A→−B→) . Thus (A→+B→)⋅(A→−B→)=0 or  A2+B→⋅A→−A→⋅B→−B2=0Because of commutative property of dot product A→⋅B→=B→⋅A→∴ A2−B2=0 or A=BThus the ratio of magnitudes A/B=1