A) parallel to \[\vec{a}\]
B) perpendicular to \[\vec{a}\]
C) parallel to the plane of \[\vec{b}\] and \[\vec{c}\]
D) perpendicular to \[\vec{c}\]
E) perpendicular to \[\vec{b}\]
Correct Answer: A
Solution :
\[(\overrightarrow{c}\times \overrightarrow{a})\times (\overrightarrow{a}\times \overrightarrow{b})=[(\overrightarrow{c}\times \overrightarrow{a}).\overrightarrow{b}]\overrightarrow{a}\] \[-[(\overrightarrow{c}\times \overrightarrow{a}).\overrightarrow{a}]\overrightarrow{b}\] \[=\overrightarrow{a}[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{c}]-0=\overrightarrow{a}[\overrightarrow{a}\,\overrightarrow{b}\,\overrightarrow{c}]\] \[\therefore \]\[(\overrightarrow{c}\times \overrightarrow{a})\times (\overrightarrow{a}\times \overrightarrow{b})\]is parallel to\[\overrightarrow{a}\]
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