d
The formula for \(|\vec{A}+\vec{B}|^{2}\) is,

\(|\vec{A}+\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}+2 \vec{A} \cdot \vec{B}\)

\(=A+B+2 A B \cos \theta\) And The formula for \(|\vec{A}-\vec{B}|^{2}\) is,

\(|\vec{A}-\vec{B}|^{2}=|\vec{A}|^{2}+|\vec{B}|^{2}-2 \vec{A} \cdot \vec{B}\)

\(=A+B-2 A B \cos \theta\)

It is given that,

\(|\vec{A}+\vec{B}|^{2}=|\vec{A}-\vec{B}|^{2}\)

\(A+B+2 A B \cos \theta=A+B-2 A B \cos \theta\)

\(4 A B \cos \theta=0\)

\(\cos \theta=0\)

\(\theta=90^{\circ}\)