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 A2 - B2 = 0
A = B (∵ \(\vec A.\vec B=\vec B.\vec A\))