a [a (a b)] is equal to - Vidyadip

MCQ

$a\times [a\times (a\times b)]$ is equal to

A
$(a \times a\,)\,.\,(b \times a)$
B
$|a \times d{|^2}$
C
$[a\,.\,(a \times b)]\,a$
✓
$(a.\,a)\,(b \times a)$

✓

Answer

Correct option: D.

$(a.\,a)\,(b \times a)$

d
(d) $a \times [a \times (a \times b)] = a \times \{ (a\,.\,b)\,a - (a\,.\,a)b\} $

$ = (a\,.\,b)(a \times a) - (a\,.\,a)(a \times b)$$ = (a\,.\,b)\,0 + (a\,.\,a)(b \times a)$

$ = (a\,.\,a)\,\,(b \times a)$.

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