[b c , ,c a , ,a b] is equal to - Vidyadip

MCQ

$[b \times c\,\,c \times a\,\,a \times b]$ is equal to

A
$a \times (b \times c)$
B
$2\,[a\,b\,c]$
✓
${[a\,b\,c]^2}$
D
$[a\,b\,c]$

✓

Answer

Correct option: C.

${[a\,b\,c]^2}$

c
(c) $[b \times c\,\,\,c \times a\,\,\,a \times b]$$ = (b \times c)\,.[(c \times a)\, \times \,(a \times b)]$

Let $a \times b = d$

so , $(b \times c)[(c \times a) \times d] = (b \times c)[(d.\,a)c - (d.c).a]$

$ = (b \times c)[a.(a \times b).c - (a \times b)c.a]$

$ = (b \times c)[a\,b\,c]a = a.[b \times c].[a\,b\,c]$

$ = [a\,b\,c][a\,b\,c] = {[a\,b\,c]^2}$.

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