For the sum (A→+B→) , difference (A→−B→) and cross product (A→×B→) of two non zero and  non linear vectors A→ and B→ to be mutually perpendicular, the compulsory condition is

Let A→=a1i^+a2j^+a3k^ and B→=b1i^+b2j^+b3k^ Given that A→+B→ is perpendicular to A→−B→  i.e., (A→+B→) . (A→−B→)=0 or  (a1+b1)(a1−b1)+(a2+b2)(a2−b2)+(a3+b3)(a3−b3)=0 or a12+a22+a32=b12+b22+b32 or |A→|=|B→| Cross product of A→ and B→ is perpendicular to the plane formed by A→ and B→  or A→+B→ and A→−B→