Answer:
(b, d) \[|\vec{A}+\vec{B}{{|}^{2}}\,=\,|\vec{A}-\vec{B}{{|}^{2}}\]
\[\Rightarrow
\,(\vec{A}+\vec{B})\,.\,(\vec{A}+\vec{B})\,=\,(\vec{A}-\vec{B})\,.\,(\vec{A}-\vec{B})\]
or \[4\,\vec{A}.\,\vec{B}=0\]
or \[\vec{A}.\vec{B}=0\]
or \[AB\cos \theta =0\] if \[\theta
={{90}^{o}}\] or
either
\[|\vec{A}|\,=0\]
or \[\,|\vec{B}|\,=0\]
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