Let a→,b→ and c→ be three $$non-coplanar$$ vectors and r→ be any arbitrary vector. Then (a$$→×b→$$)×(r$$→×c→$$)+(b$$→×c→$$)×(r$$→×a→$$)+(c$$→×a→$$)×(r$$→×b→$$) i, always equal to

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Let a→,b→ and c→ be three $$non-coplanar$$ vectors and r→ be any arbitrary vector. Then (a$$→×b→$$)×(r$$→×c→$$)+(b$$→×c→$$)×(r$$→×a→$$)+(c$$→×a→$$)×(r$$→×b→$$) i, always equal to

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(a$$→×b→$$)×(r$$→×c→$$)=((a$$→×b→$$)⋅c→$$)r$$→−$$((a$$→×b→$$)$$⋅r→$$)$$⋅c→$$=$$[a→b→c→]r→−[a→b→r→]c→ Similarly, (b$$→×c→$$)×(r$$→×a→$$)=$$[b→c→a→]r→−[b→c→r→]a→ and $$(c$$→×a→$$)×(r$$→×b→$$)=$$[c→a→b→]r→−[c→a→r→]b→⇒ $$(a$$→×b→$$)×(r$$→×c→$$)+(b$$→×c→$$)×(r$$→×a→$$)+(c$$→×a→$$)×$$(r$$→×b→$$)=3$$[a→b→c→]r→−$$($$[b→c→r→]a→$$+$$[c→a→r→]b→$$+$$[a→b→r→]c→$$)=3$$[a→b→c→]r→−[a→b→c→]r→$$=2$$[a→b→c→]r→

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Let a→,b→ and c→ be three non-coplanar vectors and r→ be any arbitrary vector. Then (a→×b→)×(r→×c→)+(b→×c→)×(r→×a→)+(c→×a→)×(r→×b→) i, always equal to

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