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Prove thet $ \overrightarrow{a}\times( \overrightarrow{b}\times \overrightarrow{c})+ \overrightarrow{b}\times( \overrightarrow{c}\times{a})+ \overrightarrow{c}\times( \overrightarrow{a}\times \overrightarrow{b})=0$

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  • Vector triple product $(\overrightarrow a \times \overrightarrow b) \times \overrightarrow c=(\overrightarrow a.\overrightarrow c)\overrightarrow b-(\overrightarrow b.\overrightarrow c)\overrightarrow a$ $\overrightarrow a \times (\overrightarrow b \times \overrightarrow c)= (\overrightarrow a.\overrightarrow c)\overrightarrow b - (\overrightarrow a.\overrightarrow b)\overrightarrow c$
LHS = $ (\overrightarrow a.\overrightarrow c)\overrightarrow b-(\overrightarrow a.\overrightarrow b)\overrightarrow c+(\overrightarrow b.\overrightarrow a)\overrightarrow c-(\overrightarrow b.\overrightarrow c)\overrightarrow a+(\overrightarrow c.\overrightarrow b)\overrightarrow a-(\overrightarrow c.\overrightarrow b)\overrightarrow b$
$ = (\overrightarrow c.\overrightarrow a)\overrightarrow b-(\overrightarrow a.\overrightarrow b)\overrightarrow c+(\overrightarrow a.\overrightarrow b)\overrightarrow c-(\overrightarrow b.\overrightarrow c)\overrightarrow a+(\overrightarrow b.\overrightarrow c)\overrightarrow a-(\overrightarrow c.\overrightarrow a)\overrightarrow b$
= 0 = RHS


answered Jun 8, 2013 by thanvigandhi_1
edited Jun 23, 2013 by thanvigandhi_1

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