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→) = 0or   A2+B→.A→  −  A→.B→ − B2  =  0  Because of commutative property of dot productA→ .B→ = B→.A→∴   A2−B2 =  0  or  A  =  BThus the ratio of magnitudes AB = 1