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Question Number 48993 by Raj Singh last updated on 01/Dec/18

Answered by $@ty@m last updated on 01/Dec/18

$$Inordertosavetime,$$$$I^{\prime }llwrite\mathrm{a}insteadof\overrightarrow{\mathrm{a}}$$$$LHS=\left[a\times bb\times cc\times a\right]$$$$=\left(a\times b\right).\left\{\left(b\times c\right)\times \left(c\times a\right)\right\}$$$$=\left(a\times b\right).\left\{d\times \left(c\times a\right)\right\}whered=b\times c$$$$=\left(a\times b\right).\{(d.a)c-(d.c)a\}$$$$=\left(a\times b\right).\{\left[bca\right]c-\left[bcc\right]a\}$$$$=\left(a\times b\right).\{\left[bca\right]c-0\}\because \left[bcc\right]=0$$$$=\left[bca\right](a\times b.c)$$$$=\left[bca\right]\left[abc\right]$$$$=\left[abc\right]\left[abc\right]$$$$={\left[abc\right]}^2=RHS$$

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