As the vector \(\vec A+\vec B \) and \(\vec A-\vec B\) are perpendicular to each other, therefore

\((\vec A+\vec B).(\vec A-\vec B)=0\)

\(\vec A.\vec A-\vec A.\vec B+\vec B.\vec A-\vec B.\vec B=0\)

or A^{2} - B^{2} = 0

A = B (∵ \(\vec A.\vec B=\vec B.\vec A\))