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