A) \[\overrightarrow{a}\bot \overrightarrow{b}\]
B) \[\overrightarrow{a}|\,|\overrightarrow{b}\]
C) \[\overrightarrow{a}=0\]and\[\overrightarrow{b}=\overrightarrow{0}\]
D) \[\overrightarrow{a}=\overrightarrow{0}\]and\[\overrightarrow{b}=\overrightarrow{0}\]
E) cannot be determined
Correct Answer: D
Solution :
\[\because \] \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{0}\] \[\Rightarrow \]\[\overrightarrow{a}\] is parallel to\[\overrightarrow{b}\] Also, \[\overrightarrow{a}.\overrightarrow{b}=0\] \[\Rightarrow \]\[\overrightarrow{a}\]is perpendicular to \[\vec{b}\] which is possible only, if \[\overrightarrow{a}=\overrightarrow{0}\]or \[\overrightarrow{b}=\overrightarrow{0}\]
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