The value of \[(\overrightarrow{A}+\overrightarrow{B})\,\times (\overrightarrow{A}-\overrightarrow{B})\] is [RPET 1991, 2002; BHU 2002]

• A.                 0             
• B.                 \[{{A}^{2}}-{{B}^{2}}\]
• C.                 \[\overrightarrow{B}\times \overrightarrow{A}\]            
• D.                 \[2(\overrightarrow{B}\times \overrightarrow{A})\]