[(a$$→×b→$$)×(b$$→×c→$$) (b$$→×c→$$)×(c$$→×a→$$) (c$$→×a→$$)×(a$$→×b→$$)] is equal to (where$$ a→,b→ and c→ are $$non-zero$$ $$non-coplanar$$ $$vectors)

Correct option is 3[a→b→c→]4

Questions

$[(\vec{a} \times \vec{b}) \times (\vec{b} \times \vec{c}) (\vec{b} \times \vec{c}) \times (\vec{c} \times \vec{a}) (\vec{c} \times \vec{a}) \times (\vec{a} \times \vec{b})]$ is equal to (where $\vec{a}, \vec{b} and \vec{c}$ are non-zero non-coplanar vectors)

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detailed solution

Correct option is C

[(a→×b→)×(b→×c→) (b→×c→)×(c→×a→) (c→×a→)×(a→×b→)]=[[a→b→c→]b→ [a→b→c→]c→ [a→b→c→]⋅a→]=abc3[b→ c→a→]=[a→b→c→]4

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[(a→×b→)×(b→×c→) (b→×c→)×(c→×a→) (c→×a→)×(a→×b→)] is equal to (where a→,b→ and c→ are non-zero non-coplanar vectors)

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$[(\vec{a} \times \vec{b}) \times (\vec{b} \times \vec{c}) (\vec{b} \times \vec{c}) \times (\vec{c} \times \vec{a}) (\vec{c} \times \vec{a}) \times (\vec{a} \times \vec{b})]$ is equal to (where $\vec{a}, \vec{b} and \vec{c}$ are non-zero non-coplanar vectors)