If a→,b→ and c→ are $$non-coplanar$$ vectors a→×c→ is perpendicular to a→×(b$$→×c→$$) then the value of [a→×(b$$→×c→$$)]×c→ is equal to

Question

If a→,b→ and c→  are $$non-coplanar$$ vectors a→×c→ is perpendicular to a→×(b$$→×c→$$)  then the value of [a→×(b$$→×c→$$)]×c→ is equal to

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Given that   a→,b→ and c→  are $$non-coplanar$$ vectors  Thus, [a→b→c→]≠$$0----iagain$$ a→×(b$$→×c→$$)⋅(a$$→×c→$$)=0or$$  [$$(a$$→⋅c→$$)b$$→−$$(a$$→⋅b→$$)c$$→]⋅$$(a$$→×c→$$)=0or$$  $$(a$$→⋅c→$$)[b→a→c→]$$=0or$$  (a$$→⋅c→$$)=0$$ Hence, a→ and c→ are perpendicular. $$---iia$$→×$$(b$$→×c→$$)=(a$$→⋅c→$$)b$$→−$$(a$$→⋅b→$$)c$$→or   [a→×$$(b$$→×c→$$)]×c→$$=0$$→

If $\vec{a}, \vec{b} and \vec{c}$ are non-coplanar vectors $\vec{a} \times \vec{c}$ is perpendicular to $\vec{a} \times (\vec{b} \times \vec{c})$ then the value of $[\vec{a} \times (\vec{b} \times \vec{c})] \times \vec{c}$ is equal to

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If a→,b→ and c→ are non-coplanar vectors a→×c→ is perpendicular to a→×(b→×c→) then the value of [a→×(b→×c→)]×c→ is equal to

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If $\vec{a}, \vec{b} and \vec{c}$ are non-coplanar vectors $\vec{a} \times \vec{c}$ is perpendicular to $\vec{a} \times (\vec{b} \times \vec{c})$ then the value of $[\vec{a} \times (\vec{b} \times \vec{c})] \times \vec{c}$ is equal to