Three vectors \[\overrightarrow{a},\,\overrightarrow{b}\]and \[\overrightarrow{c}\] satisfy the relation \[\overrightarrow{a}\,.\,\overrightarrow{b}=0\] and \[\overrightarrow{a}\,.\,\overrightarrow{c}=0.\] The vector \[\overrightarrow{a}\] is parallel to [AIIMS 1996]

• A.                 \[\overrightarrow{b}\] 
• B.                 \[\overrightarrow{c}\]
• C.                 \[\overrightarrow{b}\,.\,\overrightarrow{c}\]   
• D.                 \[\overrightarrow{b}\times \overrightarrow{c}\]